That's essentially what I'm suggesting. If they can't cite a specific regulation that is being violated and, despite that, still cannot explain why they gave it a code (any code, let alone a C2), you might perhaps be able to persuade them that they should 'remove it'. You could also 'threaten them' (or even do it!) that you might get another EICR done, by someone else, 'to compare'! If you just let them get away with doing, and charging you for, work they have invented the need for (possibly incorrectly), you will not have done yourself a service!You are right John but at this point I have an almost clean certificate to give the buyer. One or two C3s seem to be par for the course. I'm sure they could find more if they looked closely. Persuading them that the downlights are not a violation would be the best outcome.
As I said before, even if remedial work needs doing, I would at least try telling the prospective buyer that it was always the case that the house was being sold 'as seen' and that the asking price already took into account the fact that some work would be needed (at the buyer's expense).If they won't back down then a few hundred pounds spent to close the sale would be worth it.
Kind Regards, John