Redbeard

If I were doing something like that I would use Pro Clima's Intello (which is vapour-closed in low temperatures but becomes slightly vapour-open as te weather warms up, allowing 'dumping' of any accumulated moisture) as VCL, not the foil on PIR, so just make the wall as thick as you need to get the U value you want without the PIR, then it could 'breathe' (a bit) both ways instead of being 'blocked off' on the inside.

Sorry, that's drivel!! Reaching the dew-point on the inside of the external wall is more likely with thicker insulation, not thinner. I know that! I think my brain must have gone on holiday for a few minutes... Oops! Try this: I would not recommend having no insulation at all in the shutter-boxes. If you can use a high-grade insulant (such as the aerogel you referred to) to ensure that the surface is warmed up sufficiently in the shutter-boxes for condensation not to occur then (though the insulation value may still be cr*p compared to the rest of the newly-insulated wall, you may avoid a local mould problem inside the shutter-boxes.

Welcome! Showing that an impermeable insulant works is generally done with the aid of a 'Glaser Method' condensation risk assessment (henceforth CRA so I don't have to type that again). Glaser method is the British Standard method, still, AFAIK. It is not a 'dynamic' tool and is a bit of a blunt instrument. Again, AFAIK, it always did assume, and I think still assumes that all moisture in a wall comes from inside (in the form of water vapour). Therefore a sheet of foil will stop all moisture and everything will be hunky dory. Each of your composite boards has a VCL. Where is the VCL at the joint? I have favoured wood-fibre (and a request for a waiver on the U value) for a long time, but if I was doing PIR for clients I would use 'raw' PIR at 50mm, taped at all joints and perimeters, battens to fix it to the wall and a further 25mm PIR before plasterboard. You have to be really picky to get the VCL right. I prefer WF which has no VCL. No VCL = no VCL to get wrong. Just a pedantic point -sorry! - you say 'high U value'. High insulation value, which is a low U value. Also, to get 0.3W/m2K on a solid brick wall you will need a board of about 70mm (60 insulation and 10ish plasterboard) so your shutters won't work anyway. What thickness is your builder proposing? Who is doing the Building Control application. (In case it has not been mentioned, you need one.) You could claculate the area-weighted U value so that you could have 'fat' insulation away from your shutter boxes and thin at the boxes, but you would need to be sure that the thin insulation would not give you a dew-point. I am not sure how that would help? Do you think your bricks leak water? If they do, they'll leak with a thin thing or a thicker thing attached to them. Re the bathroom XPS will give you a VCL (the XPS is its own VCL) which you need, unless you use Wood Fibre (which is not recommended for wet rooms). But thin board won't achieve the target 0.3W/m2K U value. I hope this sounds positive, not negative! Queries welcomed.

I have done something vaguely similar, but with wood fibre. Just stagger the outside and inside verticals and make it as 'fat' as you need to get your desired U value net of the timber fraction. In my case the external members were structural and the internals not so, but it can be either way round, or indeed the load can be shared.

Beading, mesh, render I'd normally have said EWIstore... Do you feel they are expensive for those as well as for EPS? Obviously let us know, please, if you find somewhere cheaper.

I second @marshian's comment re the chipboards weetabix/digestive biscuit. I would not put chipboard within a mile of a wet room, but I realise that opinions vary. But cut out that soggy bit, please!

How are your lungs? I would not like the idea of 'boxing up' that much mould. As I said before I don't like the other alternative (treating with effectively chlorine bleach) much more. Get shot of anything with a hint of mould on it and splice in new.

The mould-ridden plasterboard we can see - Is that the back of the wardrobe? The last 2 pics suggest that the wardrobe has its own (hardboard?) back. So has the wet got through that plasterboard and then hit the integral back of the wardrobe? Is there any space between the 2? I'd like to understand the 'mechanism'. You can either jettison the mould-affected timber or treat it with fungicide - possibly based on chlorine bleach. With that as my option I'd choose replacing the timber.

OK, I'll chip in in the light of the above. Obviously none of us (except the OP) has seen or felt the surfaces but, as it's lime, you could consider something like Baumit RK70 - maybe with mesh; it's early and I have not thought that through enough yet. First stab is yes, rather than no, to mesh. And if you want a really smooth finish (think silk gloves) use Baumit Kalkin Glatt - goes on extremely thin, almost like a polish, so the RK70 has to be good. I'm not advertising for B----t, I just used the stuff for 10+ years with great success and I am not a plasterer. Other companies do lime products that do a similar job but I have not used them enough to be used to them. I note that you refer to Blue Grit and PVA. If the existing surface is very friable then no amount of nice lime plaster is going to hold onto the wall, necessarily. If it's sound but pitted, perhaps do something like I have suggested, without 'artificial aids'. You could do a 'test piece' of both... These lime products are not generally available at mainstream merchants, but they are available easily from specialist merchants.

If you do have bigger gaps cut down each side of the joint to the base of the PIR, so you have an open V with the wide (not that wide!) part on the top of the PIR, facing you. Then it is quite an easy job to start foaming at the bottom of the V and slowly bring the nozzle up till you have filled to the top. Of course you can stop before you reach the top as each squirt expands, but knowing when to stop takes a bit of experimentation. The tape over as VCL. I prefer to use air-tightness tape rather than foil tape.

I have never used them but I believe others on here have used: https://www.daemmstoffhandel.de/de/luftdichtigkeit-dampfbremsen/feuchtevariable-dampfbremsen-73/. I don't know the practicalities, but someone who has used them may chip in.

I'm not quibbling with that as a general principle, but it was my N-facing one which 'died', not the W-facing one installed at the same time which gets extremely hot in the afternoon sun (even as I type, in early March).

Oww! Yes, definitely failed unit. I'm gloomy enough about one of mine failing in year 11 of a 10-year warranty 😞, but yes, you should be covered without question. Who installed them - you or the supplier?

Any metal fabricator should be able to make you what you need. Try EWIStore: https://ewistore.co.uk/shop/external-wall-insulation/cms-810-120/

Definitely sounds like it!! What 'mechanism' are they invoking to claim that interaction/result? Sounds like a possible boat-lifting/dropping device in an area of London in the Tower Hamlets area.