Never use an accident management company, their clauses are always written so if the insurance company refuse to pay they claim it directly from you! It is the claimants duty to minimise costs such as hire, while an accident management company does the complete opposite!
There are also plenty out there currently under investigation by insurance companies and the IFB and they will delay the claim because of their investigations.
Easiest option if you are not at fault is to approach the other persons insurance. They will want to keep the cost down so will supply the hire car and get your car repaired etc.