You have probably got free legal advice attached to one of your insurance policies, give them a call.
As I understand it, the police are responsible for identification. If the wrong person should be identified that would undermine the "innocent until proven guilty" theory.
I belive the registered keeper recieves a Notice of Intended Prosecution. It is their responsibility to provide the name of the driver. If they provide the names of all possible drivers the police then have to determine who was driving......