Sorry, going on your profile it says under location "Other/Non UK" so I incorrectly assumed you were outside the UK.
If the other party has admitted liability (get this in writing if possible from their insurers) you can take your car to a garage of your choice and ask them if they will deal directly with the insurers or pay the repair cost and invoice the insurers.
I would avoid if at all possible "Claims management Companies" because the 1st thing they will do is instruct a solicitor for your "Personal Injury Claim" and provide a "Hire Car" the repair of the vehicle is never on the top of the list of priorities.
The last bump I had was settled directly with the 3rd party's insurer like it always used to be until these ambulance chasing companies came into being.This proved so much quicker and the settlement was received and the car repaired within 3 weeks at a bodyshop of my choosing.
They even gave me an extra amount for not wanting a hire car, I was more than happy with the offer and the insurers saved money which in turn keeps premiums down.