You should first contact your insurance agent to find out if any of the coverages you currently have on your motor vehicle will cover the damages caused by the motorist that backed into your auto and took off. If not, it appears in the UK you should be able to make a claim through the Motor Insurer's Bureau (MIB) and the Untraced Driver's Agreement. This 2003 agreement allows for compensation for property damage resulting from accidents where the driver is untraceable.
The MIB was formed with the Government to compensate victims of negligent uninsured or untraced motorists. There are certain steps you are required to take in order to make a claim. Your insurers should help you if you have to make a claim this way or you can find more information out yourself through www.mib.org.uk.
If in need of UK car insurance you can follow this link and look for the British Flag.