... the mere fact they don't have a transparent and prominently published procedure for resolving mistakes in their database must leave them legally wrong-footed and vulnerable?
Yes K, I was thinking of challenging along those lines. It's all very well for them to say, as they did, "we may not be able to fix this", but that attitude costs us. Yours are good words, do you mind if I use them?

Brian. The garage has spoken, at great length for over 90 minutes, to Islands Insurance but regrettably, they are not being responsive with this matter. We shall just have to wait for the HPI "investigation" whatever that involves.
Thank you all for your concern for my parents. I have actually shielded all this from them, they just think I am trying to get the best price for their car. To be honest, my mother is just glad to get it off their drive so my father can't drive it anymore!