Hi there Chris, and Welcome!
Made of wood, the entire structure is built on wooden slats, so it is already off the ground, albeit not to the extent required. The walls are pretty thin at the moment so I'd like to get some substantial sound isolation going on
If the floor is wood, and it is raised above the ground, then that is going to be one of your major weak points for isolation, regardless of how well the walls are isolated. There's also a lot of operable windows and a door in there, which are other major issues for isolation. Lots of weak points!
Space does allow for a "room in a room" construction so I think that'll be the best way to go. ... A figure in my head is around £600,
Well, space might allow for "room in a room", but budget certainly does not! At least not unless you are missing a zero or two on the end of that number...
1) Build a floor by having a felt strip around the room, then a layer of Lamella boards (or maybe boards from a company called ikoustic), then a layer of chipboard.
That would crate the wrong type of "floating floor", in the manner that is described here:
http://www.johnlsayers.com/phpBB2/viewt ... f=2&t=8173
2) Walls to be made of a layer of acoustic chipboard which is set 100mm from the existing wall, then 100mm or 75mm rockwool, then genie clips, then another layer of acoustic chipboard.
That would create a 3-leaf wall, which would be pretty lousy for low frequency isolation, as compared to a proper 2-leaf wall of the same total mass and thickness. You should never, ever build a 3-leaf wall if it is possible to do it correctly, with a 2-laf wall.
3) Ceiling to have same construction as walls. Ceiling lights will be spotlights, wires to come through holes in the chipboard and sealed with green glue
There can not be any holes in any leaves: not the floor, not the walls, and not the ceiling. All holes are major weak points for isolation. There can be one single penetration where the main electrical feed comes into the room, but from there on all the wiring and lighting must be done surface-mount. And Green Glue is not meant for what you want to use it for, either! It is a visco-elastic polymer compound, designed to be used as constrained layer damping between sheets of mass. It is not meant to be used as sealant in electrical pass-through holes.
From the photos, you already have surface mounted electrics in there: all you need to do is to take that all out, and re-install it on the inner-leaf, after you build it. You'll need to hire an electrician to do that: playing with electricity is not safe, and is probably not even legal unless you are licensed to do so.
4) It does have air con already so I'm planning on re-housing it inside the room. I believe this will circulate air effectively. I will use Green Glue to seal the air con pipes.
You will have to design silencer boxes on the air ducts, and once again Green Glue compound is not a sealant: that's not what it is meant for.
6) Cover the walls & ceiling with grey carpet,

Umm.... carpet is about the worst possible "treatment" you can put in a studio. It does the exact opposite of what is needed, acoustically. Which is why you practically never see it used on walls, floors or ceilings in professional studios! If you do see carpet in a pro studio, you can pretty much bet that it isn't normal carpet at all, but rather is acoustic carpet that is hiding the real treatment behind it....
7) Floor to have some kind of nice carpet.
Ditto! See above. If you carpet your room, it will end up sounding dull, honky, cavey, "thin", lifeless, and very unpleasant.
Does this sound/look like I'm on the right track?
No.
Do I still need genie clips if the wall is detached from the main wall?
Not only do you not need the genie clips, you also do not need the third leaf! You need two leaves, only two leaves, and nothing but two leaves.
Does the ceiling construction sound correct?
No. The ceiling needs to be 2-leaf construction too.
What is the best way to join the walls to the floor to ensure structural integrity? Also the ceiling to the walls?
You'll need to get a copy of your local building code to answer that. It will describe what methods are permitted, and those are the methods you'll have to use, or it won't pass inspection. It won't even get approval if the materials and methods don't meet code. And since this is already an elevated structure, you are going to need to hire a structural engineer to tell you what you can and cannot do safely, and what type of reinforcing will be needed under the building to support the huge amount of extra weight you'll be adding to it.
I'd also suggest that you buy two books: "Master Handbook of Acoustics" by F. Alton Everest (that's sort of the Bible for acoustics), and "Home Recording Studio: Build it Like the Pros", by Rod Gervais. Those will set you on the right track to do what you want to do, safely, correctly and properly. Between them, those two books will eat up about 10% of your budget, which is another reason why you seriously need to reconsider that. If buying a couple of books so you can learn the most basic concepts and methods is going to take a large chunk out of your budget, then that should tell you right away that the budget is very much inadequate.
- Stuart -