Hello, I am a solicitor with 20 years experience. I wlll try to answer this for you.
OK there is no reason to concede the case just because you didn't have insurance. Sure, you can be prosecuted for no insurance but that would be by the police and not by the insurance company and there is a good chance that the police will not be interested as this was some time ago ( the sentence is 6-8 points plus a fine).
You can instruct a solicitor but this is probably a small claim which means that even if you win you will not get your costs back. You could defend it yourself, and counter claim for your losses. Why do they say it is your fault?