Chilipea I would definitely encourage you to use a solicitor. If your case is as good as you say and the company has accepted responsibility then the company will be responsible for paying all your legal costs.
My DD was severely injured and left with a disability after a road accident, where the car that caused the accident drove off and no-one got his number. On the advice of a solicitor friend we found a local firm of solicitors who had a partner who specialised in personal injury, and it was the best thing we ever did.
He explained everything to us and said we would only be responsible for legal charges if we lost our case, not something you need to worry about as the company has admitted responsibility. He commissioned professional medical reports on the extent of DDs injury and when these doctors saw DD and discussed the ramifications that would result from her injuries they raised all kinds of issues that we never thought about.
At first her claim was turned down, our solicitor helped us go to appeal and the adjudicator slammed the Motorist's Insurance Bureau for rejecting her claim saying she was the entirely innocent victim of someone elses bad driving and they should pay up.
The solicitor then negotiated with the insurance bureau to maximise her compensation. Thanks to his help with getting full medical reports and negotiating her compensation, she got a significantly better payout than we ever expected. Mind you, she has to live with a badly scarred and disabled right arm for the rest of her life, and that is a significant disability when you are right-handed.
Without his help DD would have got nothing.
I really would advise you to make an appointment with a local company of solicitors who has a partner that specialises in personal injury, and that is important. Do not go to one of the no win/no fee solicitors, especially in a case like yours where responsibility has been admitted. You shouldn't need to pay fees and you will end up with a higher compensation payment.
If you would like to discuss this further feel free to PM me.