How about ANPR (extra cameras on the system already in place for the congestion charge) enforced by immediate loss of cab license unless there is a very good excuse.
Would a good excuse be that the passenger in the cab required to go to the destination in Oxford Street or similar. What if the taxi had a disabled passenger in the cab with a wheelchair? the camera would pick up that the cab had entered the restrictred area but how would the cabbie prove the passenger was disabled?