'Back in the day' when the UK claims system had not caught up with 'the States' there were not that many solicitors working on a 'no win no fee' basis. In those days Legal cover was probably worth it. Nowdays, if you pick a reputable longstanding firm of solicitors experienced in road traffic collision personal claims, and your case is water tight (which yours appears to be) the claim for lost wages, hire cars, medical expenses, clothing, physical hardship, mental hardship, loss of earning / loss of full mobility for the rest of your life etc etc is a walk in the park. An initial consultation for advice is usually free...you just need to check.
When the facts are clear the other side will want a quick out of court settlement (about 90% of these types of claim are settled out of court). However, where there is significant injury, as in your case, the major 'monetary' part of a claim can be how the injuries will effect your quality of life and earning abilities for the rest of your working life. The medical evidence from 'an expert' is therefore very important and it is this area where the solicitors earn their keep.
I am not going to advise anyone not to take out Legal Cover. If you have a good Legal cover company (and you would expect your 'Classic event' based insurance company would only use a good company...clearly not), it can take a lot of the leg work out of sorting your own solicitor. But once the solicitor is on board the procedure is just the same.
You have friends who have advised you in these matters but others my not be so lucky. I have provided my take on the issue to give others a 'heads up' on how the system works..or doesn't work.