who supplied the car first of all?
was it "your" insurance company?
was it "their "insurance company?
was it the "garage" that the car went to to get inspected?
was it one of the "claims people" who called you after the event?

once you sort this out, then you can figure out who authorised them to give it to you

in my case they wanted £3k as i'd had a car for 2 months and put 4,000 miles on it

when it came to it though, the other persons insurance company were playing silly buggers and i said at the time that when i called my insurance company, i had another call from someone else afterwards stating that my insurance company had called them as i wasn't allowed a courtusy car under my policy but, due to the personal injury aspect, i would be given one

they then argued that my car was roadworthy after the accident, i argued that, seeing as i could not open the rear door, i would be unable to carry a car seat or rear seat passengers legally of safely

they coughed up