Hi there Ben, and Welcome!
I have NO idea how I missed your first post for so long!

I just found it now, while looking for something else. Sorry about that! But as they say, "Better late than never"... I suppose!
Garage 1 is to be converted to contain equipment for recording and mix down. Ideally I’d to keep this room mixed use (e.g. hang out with friends and kids/man cave), but it’s something I’ve got time to give some thought to (and potentially talk myself into doing something a little more drastic).
It seems like you want to make this into what many people call the "control Room": the room where you actually sit down at the console, with the speakers in front of you, and do the real tracking, mixing, and perhaps mastering? If so, yes, you could combine that with a "hang out" room... to a certain extent!
The thing is that control rooms ("CR") need to have totally neutral acoustics, for obvious reasons. Since that's the room where you make critical decisions about the mix, and obviously want the result to be as good as it can be, then clearly the room cannot be permitted add anything to the sound coming form the speakers, and it also cannot take anything away: it cannot "color" the sound in any way. It must simply transmit the sound that leaves the speakers, directly to your ears, without changing it any way. That sounds simple, but is very far from simple. It requires careful design, careful construction, and careful treatment. Which means that the "other" things you might want to have in there to make it into a hang-out room, or man cave, must be carefully chosen and carefully positioned so as not ti interfere with the basic purpose of the room, which is simply to be neutral.
For example, let's say you wanted to hang a decorative bar mirror on one of the walls, with the logo of your favorite brand of beer on it (or soda, or pizza, or whatever)... well, you can't just decide to do that! You would have to carefully consider the possible locations where you could put that mirror such that it does not create any acoustic reflections that would get back to your ears, and "muddy up" the pristine sound from your speakers. You would also have to position it such that it is symmetrical with some similar object on the other side of the room, because you cannot allow the left half of the room to be acoustically different from the right half: the room must be symmetrical. If not, then your left ear hears something different than what your right ear hears, you'll try to compensate in the mix (subconsciously), and your songs won't sound right when played elsewhere. They will sound fine in the room, because you compensated for your room in the mix, but in other places that did NOT need any compensation (your car, your iPhone ear buds, your living room, the club, church, and all other locations), the song will sound "skewed", because you built into the mix a correction that is ONLY needed in one single location on the planet: inside your non-symmetrical room!
Garage 2 is to be converted into a sound-proof live room or recording drums, bands, rehearsing, etc, using a room within a room construction.
OK, fine, but I'm wondering why you didn't mention isolation for the control room, which will need it just as much as the live room!
As a result of the above work, there will be a small loft space created. If possible, this should be made available for storage, or preferably a small den for the children to hide away in, but this is another thing to think about over the next few months.
Not sure I understand that: Are you saying that, in addition to building the studio inside the triple garage, you will also be building a loft / attic above the triple garage? Adding something that does not exist at present? That will complicate your isolation plans a bit...
I am currently not in possession of a sound meter, though I should be in 1 month.
Much to my shame, that month has gone by already, so I assume that you now have the meter, and have done some measurements?
The levels for Garage 1 are to be confirmed, depending on decisions on room usage.
You said that it is supposed to be a control room, so assume typical 85 dBC levels, occasionally peaking at 100 or so.
I am quite respectful noise wise, and so haven’t done anything yet that has created enough of a racket to irritate my neighbours enough to establish what their tolerance may be.
When Maureen is out there doing her gardening one day, sit in your future control room as it is right now, and edit a song at 85 dB with occasional 100 dB peaks, in typical fashion: repeating the same small segment of some part of the music, over and over and over, while you tweak various aspects of it, such as EQ, dynamics, adding and removing instruments, adding effects, modifying effects, etc... then after a few hours of that, go ask Maureen if she enjoyed your creativity...
I would like to aim for as high a reduction of levels as is achievable, perhaps 60db (to be confirmed with sound meter readings).
60 dB TL should be achievable. It's a lofty goal, but not impossible if you have a decent sized budget.
Local traffic - closest road is busy and perhaps 30 meters away
You'll need to measure the level AND the spectrum of the noise coming off that road. Important.
Air ambulance – the house is very close to the hospital, and so the helicopter goes overhead quite frequently but randomly. I will record the level once I have a meter.
You and me both! I also live a couple of blocks to a hospital that has a chopper. They were careful in selecting it, and got a very quiet one... but it still makes a lot of noise when it takes certain flight paths in and out. So I'm very well aware of what that sounds like. Here too you will need to measure spectrum as well as level. There can be a very significant low frequency element to a helicopter's sound: There's a reason why they are called "choppers"... because of that low frequency "chopping" sound as the rotor blades repeatedly cut off and expose the engine sound and exhaust sound, as they whip around, modulating it.
Speedway – The Speedway is close enough (but not actually that close) that you can hear it very well in bed at night. I will record the level once I have a meter. I can’t imagine that I can protect from the rumble
Rumble? From a speedway? You must live REALLY close! Those cares are fairly light, the tracks are fairly smooth, and the cars go fairly fast (duh!), so there's a huge amount of mid and high frequency noise, but not a lot of rumble beyond the track itself. Unless maybe they race trucks there? Top-fuel? Demolition derby? Monster trucks? I'm trying to think of what types of motor sport would produce significant rumble at a distance from the track...
Budget
I would like to complete Garage 2 for ~£5,000, but if planning indicates that this will cost more, I would rather spend the time required to acquire the additional funds and do the job properly.
Think of it the way: this is going to cost roughly the same as converting a garage into a good quality "granny flat", complete with kitchenette and bathroom, with all that that implies: Call around a few local building contractors, and ask for a very rough estimate of what it would cost to convert each of those garages into a self-contained granny flat. Add 10%-20%, and that's roughly where your budget should be. Another way of looking at it is per square meter of floor area: I have a couple of customers in the UK with whom I am working at present on studio designs, in various stages, and it seems like the going rate for a full "ground up" studio build is around ₤ 1,000 -1,500 per square meter, and a "garage build-out" seems to cost in the region of ₤ 400 to 800 per square meter, give or take a chunk. That's the range you should be looking at. Higher for the LR (Live Room) side, lower for the CR side, but still in that range. You have about 22 m2 that you need to deal with, so do the math
Those are realistic numbers, taken from several on-going projects in your country.
Time and resources
If possible I would like to complete Garage 2 within 6 months.
I plan to do most of the work myself (or with the help of friends as required). My time is limited to what time I can find on evenings and weekends balanced with spending time with my wife and children.
I intend to use contractors only as a last resort for things that I am not competent or capable of doing myself.
It's a good plan, and reasonable... except for the time. I would shoot for more like a year, assuming all goes well.
Most people who haven't done this type of project before tend to underestimate both the cost and the time. In fact, I think I'll propose that as the first law of studio building: "It always takes much longer and costs much more than you ever expected"!
The garage is built on a concrete base, that the previous owner said rests on a steel base.

Why would a concrete slab need to rest on a steel base? That doesn't make a lot of sense... unless there's some type of cavity down there! Is this built on top of a basement, building, room, or something like that? In other words, what is under the "steel"? Is it just plain old mother earth, or is there something man-made down below?
with double brick from the floor to just short of the beginning of the roof beams.
Ooops...
meaning that you can climb from one garage across the top of the central workshop to the other garage
Ooops #2
There is a gap under the eaves of sufficient enough size to let ivy grow through.
Ooops #3
While I make final plans for the like room, I'd like to get started on the ceiling,
That's actually not a good approach. Many people make the mistake of starting to do things before they have a clear and complete plan in place, then end up having to undo, re-do, or just totally scrap what they did, and start over. You should first get your design for the entire studio absolutely complete, in all aspects, and only then pick up a hammer for the first time.
Do I insulate and plasterboard the roof, build a ceiling for the garage, ,do both of these things, or something else? Using the 2 leaf principle I'm currently thinking that I insulate the roof and the internal room within the room only.
Your current roof space appears to be open to the elements (oops #2, oops#2, oops #3), and probably by design, not accident. If so, then you cannot use that as the "S" in the "MSM" equation. The air cavity between your two leaves must be sealed air-tight, all around. You cannot do that with your current roof, if it is designed specifically to be ventilated. In that case, it is supposed to have air flowing under the roof deck, in order to keep it dry and free from condensation. You cannot interfere with that, unless you get the roof re-designed to be a full insulated, sealed roof that needs no air flow. That = money. = time. = complexity.
Therefore, you will probably need to seal off that area from below, and end up with a 3-leaf ceiling. Sometimes you just have to do that, and compensate for the reduced isolation in other ways.
If insulating the roof, what insulation should I use? The beams are 80mm deep, which doesn't appear to be a standard depth for insulation
If you use fiberglass, then it should have a density of 30 kg/m3, roughly. If you use mineral wool, then that should be 50 kg/m3, roughly. If you use something else, then all bets are off...
The insulation between the roof deck and the "middle leaf" ceiling should NOT fill the entire space: you do need to leave a gap there for the air flow. Check your local building code to find out home big the gap has to be, but I'd guess at least 5cm, probably 10cm.
I'm assuming whatever I do, I will have to close the gap under the eaves, but the purpose of that gap as I understand it is to let moisture out, so where would the moisture then go?
Correct! That is, indeed, the exact right question to ask: Where would it go? and the answer of course it that it would not go anywhere! It would be trapped, causing rot, mod. fungus, and eventually structural failure... Which is why you can't do that.
I have money now to get the garage door removed, and to have a contractor brick the gap up and install a new door.
Great, but don't do that yet! Put the money in the back, in a high-interest but low-risk account, while you work on the design for the next few months. You will, indeed, need to brick up that doorway, but you should not actually do it until you fully understand the implications. For example, you may need to get large structural things in there to support your inner-leaf ceiling, and find that the only way to get them in easily is through the door...
What external door types should I be investigating for the best STC ratings?
Forget STC ratings. They are no use at all for telling you how well your studio will be isolated. STC was never meant to measure such things. Here's an excerpt from the actual ASTM test procedure (E413) that explains the purpose and measurement of STC.
“These single-number ratings correlate in a general way with subjective impressions of sound transmission for speech, radio, television and similar sources of noise in offices and buildings. This classification method
is not appropriate for sound sources with spectra significantly different from those sources listed above. Such sources include machinery, industrial processes, bowling alleys, power transformers,
musical instruments, many music systems and transportation noises such as motor vehicles, aircraft and trains. For these sources, accurate assessment of sound transmission requires a detailed analysis in frequency bands.”
It's a common misconception that you can use STC ratings to decide if a particular wall, window, door, or building material will be of any use in a studio. As you can see above, in the statement from the people who designed the STC rating system and the method for calculating it, STC is simply not applicable.
Here's how it works:
To determine the STC rating for a wall, door, window, or whatever, you start by measuring the actual transmission loss at 16 specific frequencies between 125 Hz and 4kHz. You do not measure anything above or below that range, and you do not measure anything in between those 16 points. Just those 16, and nothing else. Then you plot those 16 points on a graph, and do some fudging and nudging with the numbers and the curve, until it fits in below one of the standard STC curves. Then you read off the number of that specific curve, and that number is your STC rating. There is no relationship to real-world decibels: it is just the index number of the reference curve that is closest to your curve.
When you measure the isolation of a studio wall, you want to be sure that it is isolating ALL frequencies, across the entire spectrum from 20 Hz up to 20,000 Hz, not just 16 specific points that somebody chose 50 years ago, because he thought they were a good representation of human speech. STC does not take into account the bottom two-and-a-half octaves of the musical spectrum (nothing below 125Hz), nor does it take into account the top two-and-a-quarter octaves (nothing above 4k). Of the ten octaves that our hearing range covers, STC ignores five of them (or nearly five). So STC tells you nothing useful about how well a wall, door or window will work in a studio. The ONLY way to determine that, is by look at the Transmission Loss curve for it, or by estimating with a sound level meter set to "C" weighting (or even "Z"), and slow response, then measuring the levels on each side. That will give you a true indication of the number of decibels that the wall/door/window is blocking, across the full audible range.
Consider this: It is quite possible to have a door rated at STC-30 that does not provide even 20 decibels of actual isolation, and on the other hand I can build you a wall rated at STC-20 that provides much better than 30 dB of isolation. There simply is no relationship between STC rating and the ability of a barrier to stop full-spectrum sound, such as music. STC was never designed for that, and cannot be used for that.
Then there's the issue of installation. You can buy a door that really does provide 40 dB of isolation, but unless you install it correctly, it will not provide that level! If you install it in a wall that provides only 20 dB, then the total isolation of that wall+door is 20 dB: isolation is only as good as the worst part. Even if you put a door rated at 90 dB in that wall, it would STILL only give you 20 dB. The total is only as good as the weakest part of the system.
So forget STC as a useful indicator, and just use the actual TL graphs to judge if a wall, door, window, floor, roof, or whatever will meet your needs.
Fire door, double glazed, something else? The plan is to leave a hole in the brickwork sufficient for a standard UK from door, nothing larger or fancier.
Now do you see why it is important to not rush ahead of yourself? You don't yet have a clear definition of what type or size of door you will need, so therefore you cannot decide how big the doorway will be. So therefore you cannot build the wall yet! You wold either need to chop out some of your brand new beautiful wall to fit in the actual door that turned out to be larger than you originally thought, or you'd have to call the brick-layer back again (and pay him so more money) to fill in the gap that turned out to be too large!
Not only that, but you don't even know
where in the wall to put that door! What if you built the wall with the doorway in it, but then found that you actually needed to put some very specific acoustic treatment exactly in that location, or maybe the place where your desk goes would not allow the door to open, or maybe you'd need that location for some gear, or furniture or part of the HVAC system, or...
Case in point: I'm currently designing a mastering studio for a customer in the USA, and there are some very annoying structural posts that support the floor above the space where his studio will be. I managed to figure out a way to fit a 36" door in between those posts, and I designed a desk that would work with that door location and size, for his console, DAW and mastering gear: Then he happened to mention that he already has a desk that he wants to use: a commercially built (and very nice) proper mastering desk... that happens to be bigger than what I designed! I modeled that desk in 3D, placed it in the 3D model of the studio... and discovered that the door would not be able to open properly: it would bump into the desk. So we decided that the best solution was to change the door from being a nice wide 36" door, to a slight smaller 34" door: That one will open OK. I also modified the front end of the room so the desk can be a bit further forwards, and I modified the door design as well. So all is good now. A few hours of design work, a few e-mails and images, and the problem is solved.
Now imagine what would have happened it he would have built his place, moved the desk in... and found that he could not open the door... !

That would not be a happy situation... he would either have to throw away his beloved (and expensive) mastering desk, or he would have had to knock down part of his studio, throw away a really nice (and expansive!) isolation door, build a new door, re-build part of the studio....
You get the picture.
This is not an isolated case: it frequently happens that I run into such issues when designing studios, and if you browse the forum you'll see that many members run into similar issues.
It is ALWAYS a mistake to start building before you finish designing. Always.
Posts I've read on this forum suggest that a separate door on each leaf is superior for isolation, meaning I could install the final solution now, adding the second door once there is an inner leaf to hang it on. A door that has to match the mass of double brick sounds like it's going to be very heavy on its own.
Right. Your doors WILL be heavy. And they will require multiple seals, all around. But the door does not need to be as heavy as the brick wall that it sits in. Ideally, yes, but in reality, no. It just has to be heavy enough to do the job. Si you will need to use the equations for MSM isolation to figure out how heavy that needs to be. The goal, of course, is to get your resonant frequency down an octave below the lowest tone that you need to isolate, and then to provide a high enough level of TL that meets your purposes.
PHOTOS:
The roof clearly cannot take any serious additional weight. Those are just 2x4 joists / trusses. You won't be able to hand any substantial weight from those. You'll likely need to beef them up in one way or another, to be able to hang the "middle leaf" ceiling that you need there.
the best use of the space would be to remove any interior walls and beams
Yes... assuming that they are not load-bearing (structural)! I see pillars built into those walls, suggesting that they might be load-bearing. If so, then could still take them out, but you'd need to support the load in some other way. It is possible.
I think I am safe to assume though that this would be major structural work and so is going to extend this project in time and finances beyond where I'd like it to go
It would be more expensive, yes, but it does not necessarily need to be exorbitant. I've done a couple of designs where the roof trusses needed to be modified to make the best use of the space, and it wasn't as complicated or as bank-breaking as you might imagine. It might be a possibility.
One again, sorry for not having answered sooner! Hopefully this is til timely, and useful!
- Stuart -