Your vehicle is hit by a third-party vehicle, which does not stop. By chance you have CCTV which identifies the registration of the offending vehicle. The police cannot identify the driver, it could be any one of several people and no one is owning up. The registered keeper is found, but they could not have been the driver. The vehicle was however covered under a valid policy of insurance.
The difficulty where the driver cannot be identified, and the journey is a private journey, is that it is not clear who can be sued for the negligent driving leading to the damage that you have suffered.
You wish to recover the cost of repairs to your vehicle. Traditionally you could claim off the MIB Untraced Drivers Agreement; an agreement meaning in circumstances like this (untraced driver) you can claim off the MIB scheme for your damages. This, in the UK, is the normal way an untraced driver claim is recovered.
It now appears you have another option; in the recent case of Cameron v Hussain [2017]. The Court of Appeal decided, as the vehicle had a policy of insurance related to it, which complied with the Road Traffic Act 1988 S151 obligation to carry insurance against 3rd Party risk, implementing the EC directive 2009/103 which requires the U.K. to impose such an obligation on its vehicle users (i.e. they cannot avoid their insured liability for third party loss), then you can claim against the insurance company providing that cover, in spite of the fact that the actual driver cannot be identified. The EU directive sets out the requirements of a mandatory third party motor insurance policy and with other EU regulatory law significantly limits the circumstances in which an insurer can refuse to pay out.