There was an article about this in one of the bike mags recently on the "Ask the Lawyer" column, White Dalton or similar firm. If my memory serves me correctly:
Primary advice was- its your bike, your choice where it goes to.
Next, regarding these "Claims Management" companies, you have to remember that when claiming against a 3rd party, you have to be reasonable in keeping a lid on extra costs. So if your bike is worth £2000, suffers £1000 worth of damage, but you rack up £5000 in hire and storage fees, a County Court judge might not be too sympathetic to you. You lose, you pay.
A couple of real-life cases;
A mate was tipped off his bike while stationary, scratched fairing panel and can. Bike went to a main dealer, who called him 2 days later saying the insurance assessors are here, are talking about writing your bike off and taking it away. He told them to not release it, went and got it back, repaired it himself, presented the bill to the drivers insurance who paid up, no problem.
My son got knocked off his old ratbike of a Diversion, but rode it home, I had a look and reckoned about £200 in parts would put it right. Next day he had a call from the drivers insurance, offering him £400 plus a new helmet of similar value to his old one, to settle the claim. He accepted!