Well, personally i would recomend you go to a solicitor, as one can never be sure that you will get what you are rightfully owed, think of it this way, The insurance company is less likely to pay you a substantial amount in damages as a result of your non - fault Rta, the third party ins is allways going to look closely to save pounds in every direction they can (It`s a business not a charity) however the solicitors dealing with yoiur claim know this and will represent you from start to finish and as a guide line you are likely to be paid out within 4 - 6 months, So no pressure for you, but to only sign the paperwork they ask you to and generally just respond to any letters in the future that they send you, and quickly.
Hope this is of help to you
Good luck
And call them solicitors
Tony