Get the building inspector out.
Should I also invite the tax officer to inspect my bank account just in case, and my wife to check my web browser history?
But tbh, if it was my job, it would be coming down and rebuilt properly at the expense of those cow herders. Cavity issues tend to take a few years to develop.
Before I do that I want to weigh the certainty of extra cost and inconvenience in the short term (extra rent for the additional waiting time and emotional cost from not making it to our new flat this side of Christmas) with the probability of issues at some point in the future. What is that probability and what could happen and at what cost? If for argument's sake the current cost from the delay (not including emotional stress) is say £2k, and there's 50% chance that an issue will arise in 10 years that it will cost me £2k to fix, I'd rather take the chance.
So, can someone please guide me through what can happen in the future?
Is the damp going to come from moisture through condensation alone (in which case it's quite likely to happen) or will it require direct water penetration as well (which is less likely if not impossible due to the thick block+render, assuming good maintenance of the render/cracks repair etc)?
Next consideration: let's say water forms in the cavity, whatever the source. How is it going to affect me? Behind the cavity gap, there's the insulation block, behind which is a damp proof membrane, and behind it is the inner block. The only direct connection is through the wall ties. These are stainless steel and stop at about half the depth of the block. Is the concern that the water will moist the inner block and then it will travel inside?
If that's the case, then can condensation alone, traveling through the wall ties to get to the inner block cause any problems (especially when presumably at that point it will meet higher temperature from the heated interior, which will dry it)?
I agree that the job was not done properly, and the "correct" thing to do is to rebuild it. But before I do that I would like to be presented with a good explanation of what can go wrong and why, and weigh the odds. Otherwise it's choosing to be pedantic over being practical, and it's sort of cutting the nose to spite the face.