Much credit to the council though - it all seems to be going very smoothly. When I rang them up the person who deals with such things was in a meeting, so I gave some details & we waited for her to call back. Which she did, a bit later in the morning. This clearly happens often enough that they have a process - she said we could have our own garage give them a quote for the repair or it would be simpler if we went with the garage they use. So we did the latter, and a chap came out & looked at the car in the afternoon, gave the council an estimate & got back in touch with us to say the work'll be done on Thurs/Fri next week & he'd call me back on Monday with confirmation of the days & directions to the garage. We'll even get use of a courtesy car.
And even better it's not going via the insurance company. The council have some scheme that basically means providing it's not very expensive (up to £600 I think she said) they just pay it & don't claim off their insurance, so we don't need to make a claim.