Ooof. Where to start.
So firstly, you need to differenciate between 'Planning Permission' and 'Building Control/Regs'
Two separate things. So all the talk of 'permitted development' etc etc falls under planning permission, and is concerned with the outside look/appearence of the finished things, such as ridge height, dormers, roof lights etc. They don't really care what goes on inside, or the thickness/type of your insulation.. that's building controls concern.
With regards building control, there are a multitude of things as play.
Firstly, you initially talked about not getting it 'classified' as a bedroom.
Well this is a bit of a grey area that's not clearly defined. You have to decide if its going to be classed as a 'habitable space' (forget bedroom/not bedroom).
'Habitable space' was not that clearly defined when we did ours a few years ago. From my googling at the time, it depended on a few factors.
A few obvious ones are.. if there are stairs up to it (rather than a loft ladder) - then it'll definitly be classed as habitable in the eyes of building control. will it be plastered out, is there lighting and sockets etc etc.
If it is going to be habitable, then you're definitely going to have to do it to current building regs standards, i.e. head rooms, means of escape (usually this means replacing all your doors that lead onto the stairs/landings with fire doors as they don't allow escape velux's anymore and the route of escape has to be down the main staircase). And is the central heating getting extended up there.
Moving on to insulation and U values. If you're going to extend the houses heating system into the loft, then you definitly fall under the building regs for that. (regardless of the classification of the room) since you are making a previously unheated space, into a heated space, and extending the thermal envelope of the dwelling.
This will be latest Part L building regs.
https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/1133079/Approved_Document_L__Conservation_of_fuel_and_power__Volume_1_Dwellings__2021_edition_incorporating_2023_amendments.pdfSee 4.11-4.13 and 11.2 to 11.4
For the roof you'll need to hit a U value of 0.16
Usual way is to put some PIR between the rafters, what ever will fit and still leave the 50mm gap required up the back.
Then under draw with some PIR backed plasterboard. (which invariably causes issues with head room etc).
Be wary of multifoils. I'm not saying they're complete bunkum, but they are certainly not 'space saving' because in order to actually get any of the claimed U values, you need to have a decent air gap either side, and usually its in conjuction with some PIR between the rafters too. They are also a complete pain to work with (feed back from builders). Counter battens one way across rafters, then the foil, which needs nailing, as screws twist it all up, then counter battens the other way. Its more work than you may imagine and builders time costs money! PIR backed plasterboard is quick and easy to work with.
You want to aim to get as much PIR between the rafters really, to minimise the thickness of the underdrawn stuff, to give you more head room, hence the suggestion of thickening the rafters to accomodate.
PIR generally has a conductivity of 0.022 (Xtratherm, Unilin, Celotex, Ecotherm, Recticel etc).
Kingspan has a slighly lower (better) conductivity at 0.018, but is suitably more expensive.
To hit a U value of 0.16, with standard (0.022) PIR, then you'd need 120mm between your rafters and 50mm PIR underdrawn (ends up being a 62.5mm board with 50mm PIR and 12.5mm Plasterboard).
Thus your rafters would need to be at least 170 deep, to allow for the 120mm + 50m air gap.
For what its worth, I took a different approach with ours. Its a hobby room/store room, albeit a very nice one. Just got a loft ladder permenently bolted to wall up through a hatch. This will get replaced with a folding loft ladder when we sell and we'll not be able to advertise the loft room. As its not habitable.
Heating system was not extended up into the loft, so just occasionally use an electric heater up there. There was already a socket up there, so just extended the ring main with a couple more sockets (my understanding is that you can extend an existing circuit yourself, but need a Part P electrician to install an new circuit). The ceiling is insulated right across the horizontal, like a normal loft. then boarded over the top. So the loft room is not part of the thermal envelope. However, we had 75mm rafters and I elected to put 50mm PIR between them, with a 25mm air gap. I've justifed this lesser gab to myself on account of there being no felt and the gap behind is extremely well ventilated (you can see sky through a lot of it!! but doesn't seem to leak). Roof/slate will get replaced at some stage in the future I'm sure and we'll address this then.
Anyhow, good luck with it!