Friends,
It is time for me to intervene by thanking you for your comments and advice. I have found it all to be helpful and informative, even if your experiences at the hands of the insurers have not been consistent. Let me show my appreciation with an update.
My son dropped into his friendly garage to check that the car is roadworthy. Their MOT tester was only concerned to make sure that there are no sharp edges, which there aren't. So it is safe and roadworthy. They directed him down the road to a body repair shop which estimated the cost as about 30% more than he (I) bought the car for.
The other party's insurer called my son to sort things out. They indicated that they are happy to repair the car (although I don't know if they realise the repair is more than the value of the car at this stage), or to make a cash settlement. They will send an assessor round later this week. My son was careful not to hand it over to the insurer or the good advice above. My son notified his insurer, and they are happy for it all to be handled by the other party's insurer, with no loss of no-claims discount.
So far, the insurance companies have acted with integrity and have been genuinely helpful. I'll let you know the final outcome.
Lets keep the discussion friendly and respectful. We have a common cause, after all.