Was it your fault?
If not, then you're perfectly within your rights to accept a hire car off the people repairing yours and it'll be charged back to the other person's insurance. I assume it's going into VW too? They will be more trustworthy, so to speak, than one of these dodgy insurance approved Haward B'stard places.
I know this is a big money making racket and they'll stuff the other person extortionately for lending you a Micra or something, but if you need a car, you need a car.
I'd go through the paperwork with a fine toothed comb, don't accept any liability for it and give them no card details etc.