Registration number or not - you can find out the registration number fro DVLA if ARCA get the chassis number (VIN number - Vehicle Identification Number)  from the plate under the bonnet. Then you can tack the owner down using DVLAs facilities. Nail that owner and send them the bill. Someone had a car dumped on thier land not so long ago and it was amazing how fast the owner was found using these services! Hope they read this and own up but I doubt it.

John.