Hire car had to be recovered by Police-next steps?

My car is in being repaired after being hit by a drunk driver while parked (so no quibbles on fault etc).

I'm dealing with Auxillis. They provided me a hire car. Said hire car broke down on a busy road today. I called their breakdown number and was quoted an 8 hour wait. Due to where the car was, the police said they would need to sort out recovery.

Now obviously this costs money. Will I ultimately be liable to pay the recovery, will it be claimed from the breakdown cover or will it go onto the final bill Auxillis are sending over to the drunk driver's insurance?