Hy Kate
What you need to do in this instanse is report the accident to the police as soon as possible, report anything you can remember of the other driver and car, especially the make, model and vehicle registration. If you have these details in hand then its not hard to trace the driver, but this then can fall in many categories as the car could be registered on someone elses name, it could be stolen etc. But what ever the case you still can claim.
If you have no details of the driver then you will have to claim of motor insurance bureau whom fund for uninsured drivers, traced and untraced.
Traced- You have the vehicle details but the driver is not insured
Untraced- You have no details of the driver of vehicle.
But whatever the case you can claim, but mind you getting MIB to payout can be a nightmare as they can strech the whole case over 2 years, but depending on whats at stake you might consider walking down that root.
Hope that helps, if you need assistance i specialise in motor insurance claims, let me know maybe i can assist you further
Thanks
The Claims Guy