Even going down the no-win-no-fee route may be worth it. They have admited liability, and if you were awarded £1000 on a 25% fee, that's still £750, which is £425 more than currently on offer.
Also, as has been said, if the solicitor is any good they will insist on medical reports etc - all at the insurers cost as they have admitted liability - and they (should) significantly up the payout and also give peace of mind that there's no long term damage. Remember, once you settle, there's no going back for more in a couple of years when you find that somethings' not right and isn't going to get better, or will cost alot to put right.
After reading the T&Cs and accompanying forms from the solicitor, it felt like I would be selling my soul if I signed them. I didn't get a feeling that I was their principal concern, but that they would manipulate the situation so that they did as little work as possible to obtain as much money for themselves as they could.