To be honest, I did say in your other thread that I felt your claim had good prospects. The vehicle owes a greater duty of care to you than you to they, the fact you may have had a drink or two is irrelevant if it didn't contribute to the circumstances, and the motor law of Davis Vs Schrogin, whilst aimed at motorcycles, is pretty valuable to your case.
At the end of the day, no win no fee is just a way of funding a claim, and if you were not injured, then your claim up to £5k can be made in the small claims court anyway, where no legal fees are required/needed, nor is any cover for theirs.
Chase up the household insurance, but the police are not the best at assisting when they've been in a bump. Arrogant coppers who know they make impressive and unimpeachable witnesses, and that courts lap up their evidence, will routinely mess you about, not respond to requests for information and basically make life hard for you. Either that, or they're all too busy eating bacon sandwiches in the canteen to deal withthe paperwork.