Roundtuit

Come on; stop beating around the bush and say what you think 😄

Bespoke, so they can build what you want. About 18 months ago, the frame was just under £19k erected, and included timber for studs, joists and cladding, but it is quite big: effectively 3 bays plus wood store each end, and storage space up top. Still progressing at a snail's pace as a 'spare time job', but looks more like this now...

Oak frame kit, delivered and erected in 2 days. Finish at your leisure via trades or DIY!

Don't forget to factor-in a ventilated cavity behind the cladding.

Have a look at profilestore.co.uk, ventilation profiles. They do flat or angled in black at good prices. I bought some recently for proofing some cladding.

This suggests that the law may be on your side... https://www.moorebarlow.com/blog/can-a-neighbour-erect-scaffolding-on-your-property/

Scaffolding aside, are they going to need access to actually build ie brickwork/pointing etc, or can it all be done from their side?

Nah...looks off to me too. More like an a 'artist's impression', particularly as one of the kitchen above-counter sockets appears double-up through the photo montage...

That's the only one of three that made decent progress, and that's still probably the case 3 years on tbh. I did make an early mistake of using garden soil for some planting, so maybe a nutrient overdose.

Wildlife pond. 2 years and 2 months between pics.

At risk of going off-topic... then there's the upfront cost for a minimum delivery (500 litres?) to consider. I don't use oil, but I can see why people find themselves having to live in a cold house for a while.

Does it need repairing? What do you want to achieve?

Absolutely, but no easy fix without stripping back to what was supposed to be the airtightness strategy...

If you've got air circulating behind the plasterboard it could be coming from anywhere, and potentially multiple leaks; service penetrations, joist ends, window reveals, poorly taped joints etc... I'd just focus on the sockets where you can feel a problem and seal them up as best you can.

What's the wall make-up out of interest? Dot and dab? Timber frame? Service void? Which ever, I suspect the fix will the same 'sticking plaster': remove socket/back box, fill all gaps with something (foam, airtightness tape, mastic, all of the above), refit.