If liability is admitted, then its low risk so the success fee should be low. As to value, it all depends on type and severity of injury. Torn ligaments might not be simple to heal. Best bet is not to settle until there is a plateau of recovery so there is better certainty of outcome and...
Go to a law firm who specialise in this. I used a legal expense insurer panel solicitor once and they weren't great. You get a personal service with a local specialist firm.