I've just got off the phone to the insurer. The guy didn't bat an eyelid about it, and I have read anecdotal stories of people successfully claiming for this sort of thing from Direct Line, who we're with. They're sending someone to fetch the car tomorrow and take it to the preferred repairer. He offered the option of sending an engineer out to look at the car at our garage, but said that it can take much longer doing it that way. Enterprise are also going to sort out a hire car for me tomorrow - hopefully better than the asstastic Chevy Spark we got last time, but probably not. I need to get down to the garage and get the kids' car seats and my head unit and a few other bits and bobs.
The garage said they'll charge me £35 for their cursory look, which strikes me as very reasonable.
So, all things considered, this is going pretty smoothly.