Sounds to me that you've been caught in the credit hire / accident management company scam. In that you are provided with a a hire car (not a courtesy car) and the small print that you sign up to on taking the hire car commits you to paying for the hire car if the other party's insurer refuses to meet the hire cost (e.g. on the ground that they are excessive).
Hire car costs in such instances often are excessive because the accident management company "facilitates" the repairs taking (much) longer than they should do, charging very high rates in the first place (as well as trying to up the model supplied).
Check the small print of whatever you signed.
And take independent legal advice.