You may find that it is the road traffic law that prevents the 'Blues and twos' bit.
If they were to have an accident and were not correctly authorised or trained on civilian highways, they WOULD be liable. Driving for another lighted service, the Chief Constables (and ACPO) of some UK counties have stated that they would prosecute the law to their fullest ability if untrained persons (even on legitimate shouts) had an accident using the equipment - they can follow and apprehend but not necessarily with emergency lighting?? Try it and see how you get on?
They also are not permitted to contravene road traffic law so would stop as red lights – defeats the purpose really!!!!
a little more info - note only RAF mountain rescue are specified.