Thanks for everyone who offered advice, I've read the links. I talked to my doctor about the sore arm and shoulder and she said it was normal and would go away. I talked to a lawyer and thought with my American hat on that if I said I'd been hit by a Veolia lorry, had whiplash and they had admitted fault that I'd have a crowd of lawyers outside my door. They didn't care one jot! They directed me to some government reconciliation process where if you can prove you've had whiplash for 6 weeks they will give you £650 and if you lose an arm they will give you £2500. Good thing I wasn't actually hurt seriously. The soreness has now gone away.
Anyway, it looks like I will just take the money for the value of the car, which will be lower than I would like and avoid the loss of no claims discount because the other side will pay. No need for lawyers after all.