Hit by a car while cycling, driver admits blame, bad injuries, need advice re solicitors & making a claim.

Hi, sorry to just jump straight in but as a matter of urgency I could do with some advice about solicitors, their fees and making a claim in court for compensation following a bike RTA in which the driver has admitted he was at fault and has done so to the police in his witness statement.

The person who was knocked off their bike was my Mum so I'll just make that clear from the off.

A couple of weeks ago she was cycling to her Monday morning exercise class and was knocked off her bike by a car driven by a bloke who has, in short said "I can't understand how I didn't see you but I really just didn't, it was my fault and I take full responsibility for the accident".

He was filtering onto the road my Mum was cycling along from a sliproad off a motorway. He'd stopped at the top of the sliproad at the broken white line where the sliproad meets the road my Mum was on. He stopped there to check the state of the road he was filtering onto, saw a clear route forward and set off.

My Mum had cycled across the end of the sliproad (the sliproad the bloke had driven up and was waiting at the end of) moments before and when the bloke set off from his stationary position at the end of the sliproad my Mum was a few meters to the left of the bloke in the car.

The bloke set off and within a very short space of time he had driven into my Mum hitting her with the drivers front side catapulating her off her bike and into the air. He was travelling at 10mph when he hit her.

To cut a long story short my Mum was admitted to hospital and she was found to have one broken rib a punctured lung and a gash in the back of her head that went down as deep as her skull.

She was not wearing a helmet, usually she does but of course sods law being what it is the day that she doesn't wear one this is what happens. So while there is a lot that I'm sure many people reading this would like to say about the stupidity inherent in the decision my Mum took that morning not to wear a helmet I'd like to ask anyone reading this to please, with respect leave out the whys and wherefores of helmet wearing from this thread that is intended to be a genuine appeal for advice about solicitiors and making a claim following a cycling RTA.

Again, cutting things short what I would like to get some idea of is how much we can expect a solicitor to reasonably take from any award the court makes, we spoke to a solicitor today who said his fee would be a quarter of whatever is awarded, is this about normal, high or low?

Also, we have so far spoken to two firms of solicitors in our home town. Would people say we can potentially expect to receive a perfectly good service from a 'multipurpose' solicitor (I know I'm not using the right terminology here but what I mean is a solicitor that isn't a specialist in cycling accidents but also deals with other types of cases) or is it imperative that we seek out a specialist cycling accident solicitor (if such a solicitor even exists) to get the best possible outcome in a case like my Mums?

I would be massively grateful for any / all help anyone can give me with this and thanks in advance to anyone still reading at this point.

James (North Yorkshire)