injury claim? should i? who should i use?

Astaroth

Defence costs are payable if the claimant is unsuccessful or have rejected a part 36 offer and the court rules that the offer was fair.

RibenaBerry_2

The rule Missile suggests is similar to how it works in employment cases. If you bring a tribunal claim, you don't normally get costs awarded against you even if you lose. Astaroth is exactly right about costs in most cases- including PI.

A Part 36 is a formal settlement offer than the defendant makes part way through the litigation. If you don't accept the offer and then either lose, or get an award lower than the offer, then you bear the costs from (roughly) that time on. It's designed to make people give serious consideration to settlement. Your solicitor would explain all of it to you if it happened, but I thought I'd just explain Astaroth's terminology.

pardon

A no win no fee solicitor is not always the only solution. You have a very good case. I would try to get a quote from a local solicitor. If they're willing to take your case for what you think is a reasonable fee that's great otherwise I would go with a no win no fee solicitor.