In the case of a hit and run or uninsured driver causing an accident, there is no insurer to claim from. Most people assume you can do nothing and will have to claim against their own comprehensive insurance for the damage to their vehicle. By doing this you will probably pay your excess and certainly can’t claim for injuries.
However, there is a body set up to provide access to compensation for just this kind of incident. They are the not-so-well known ‘Motor Insurers Bureau‘ or MIB. The MIB investigate these claims and where applicable, provide medical rehabilitation to injured claimants and compensation payments including loss of income etc.