Redbeard

I realise you will probably be there for life, but just in case you ever need to sell, might I suggest that you try to 'buy' that 50mm? A client of mine did exactly that, though they at least knew who owned the land. In the case of a 'shared road' it may not be so straightforward to find the 'owner' to buy from.

I was typing while @JohnMo was posting. His points are very valid. Why rip out if you cannot afford to re-do? If the potential cost is completely unaffordable why not ask for a staged plan?

Welcome. What's the orientation? Is it conducive to solar? Do you have plans for PV? I assume the house is of cavity construction. is the cavity insulated? If money is tight I am not sure how keen you'll be to completely remove the bays and 'plant' new bays on top of EWI. EWI also needs care to avoid the risk of thermal by-pass via the cavities. If you were to go for internal insulation (IWI) you'd be limited as to what U value you could achieve, due to the risk of interstitial condensation. Detailing can also be tricky depending on the internal layout. On the other hand, assuming you do not own the land to the right, I'm not sure how practical EWI would be, either. Ideally you need to find a way to use one or the other, or a mixture of both. If perchance, there are 'viable' (50mm+ and 'clean') cavities and they are uninsulated, start with that, with EPS beads (not mineral wool, in my view).

The same could apply with a double-skin timber frame with much more choice of insulant and a more 'permanent' 'feel' (both of those 2 words pretty vague in meaning in this context, but clear to my old brain).

why ply? Why not plasterboard? Some of my sloping soffits have thin wood-fibre (40-50 year-old), plastered over, and almost certainly as an underdrawing to knackered lath and plaster (This year's job to remove and insulate with 260mm wood-fibre and lime plaster over (yes, had the structural calcs done!). The plaster on the aforementioned thin WF causes it to sag, so it looks cr*p.

What you describe is a hybrid Warm roof - some on top of the rafters and some between. In some circumstances there is a risk of the dew-point occurring at the interface. A condensation risk analysis (CRA) can guide you, but a colleague had a good rule of thumb: If you have two-thirds of the R value above the rafters and one-third below, the interface is unlikely to get cold enough to reach the dew-point. If I remember correctly the lambda of cellulose is (or was when I used it) 0.036W/mK, and PIR is 0.022W/mK. So for 125 cellulose it's 3.47m2K/W (actually less, as that does not take into account the 'intrusion' of the rafters) and for 100 PIR it's 4.54m2K/W, so not too far off but probably not two-thirds/one-third. A CRA (particularly if done in the WUFI software) will be more accurate. Edit: A thought: If noise is an issue why not consider rigid wood-fibre on top? 140-180kg/m3 as against about 32kg/m3 (IIRC) for PIR)?

I would not advise skimming over paper, however well-bonded it appears to be. Borrow a steamer and steam it off. 24hrs seems a v short time to leave a deeper base-coat before skimming. I'd just say leave it longer. If you can get hold of a small amount of lime putty (which lasts forever when kept under water) you can just mix it as required with plastering sand. There are specialist lime etc. suppliers not so far from Oxford.

Do you really need access? What is there to access? Wiring? Plumbing? Ductwork? I am guessing none of the above, so that leaves 'the void'. Project yourself forwards 10, 20 or 30 years and think if the necessity will ever crop up. If you think it won't, don't have a hatch. Worst case scenario is that years hence you have to cut the plasterboard and get deluged with Warmcel. Not the worst deluge in the world.

Congratulations - a big worry off your plate. Perhaps more importantly, is the house (and are the bills) comfortable?

Re the sloping roof, unless they guessed it wrong 1st time (design U value), all other things being equal (which perhaps they are not*)I cannot fathom how they get a worse U value with 150 (as-built - apparently 0.2W/m2K))than with 125mm (stated as 0.18). *Much closer rafter centres and fatter rafters (therefore larger timber fraction in the calc) in as-built than design? So this is to the pre-2022 Regs, then?

There is no discussion to be had. Not least because of that 'droop' - never mind what's hidden behind the once-wet plasterboard - they seem to be proposing to hand it back to you looking worse than it did when you bought it. Say no and stand your ground.

....and ended up with 50mm PIR (only, as far as I read) in the walls? Since SAP for new-build is a whole-house affair (with back-stop - worse - U values for each element if I recall correctly) unlike refurb, where it is 'walls must be x; roofs must be y' etc.) I am not saying 50mm PIR would not 'hack it' but it sounds like half or less what I'd have used. What was stated in the archo's dwgs? My U value calcs are only rough ('fag-packet' rather than software) but the lightweight blocks must be a lot better than the standard blocks in my default to get 0.25W/m2K. Was there really less than 50 PIR (say 100 rockwool) spec'd initially?

But I am a pessimist! And someone for whom wonder-glues rarely do what they say on the tin/cartridge/tiny tiny little tube...

My thoughts too, though it depends on how many pieces the 'piece' is in. Many people have a lot of success with epoxy. If you have the piece as a whole piece you could try drilling holes for, say, 3 dowels in the main cill, bed the dowels in epoxy in those holes, and drill corresponding, perhaps slightly oversized, holes in the broken piece, clean and 'butter' the faces with epoxy, then breathe deeply and and press together. If you are lucky the reveal could help wedge it together. Optimist's view: Done! Pessimist's view: (Just refuse to entertain that view!)

While the extension is incomplete it is the best time to chase and resolve the leaks. They will bug the hell out of you in future if you don't. I agree with @Russell griffiths that the membrane on the sloping soffits looks like standard thin poly VCL. There's a small chance it could be something else but that green is suspiciously indicative of 'Bargain Basement VCL'. I'd like Intello too. Please do not give up on leak-finding! I assume the walls are leaky too? But even if they are not, as far as the roof goes you want (a) the right membrane and (b)someone to make sure it is as tight as a tight thing from an air-tightness POV. If the reason you have given up with a/t is the difficulty of finding the holes have you thought of making a basic 'blower door' (old desk fan or car radiator fan in a lump of ply) to tape into an opening? If you de-pressurise the room you're checking then, certainly in this weather, you will feel cold air rushing in. Arm yourself with good-quality a/t tape and you're off. I am sure someone(s?) on here has posted pics of such a home-made fan. Found it: 1st post on p.4 of this: Good luck. Do not give up, and please do not let them begin to plasterboard till you are happy.