The last time I looked this up I was lead to believe that if your old MOT was still valid the car was still drivable, even with a fail, the garages Ive used never had a problem with me driving a car they had just failed.
These falures were on emmisions, so the safety of the car was never really questioned.
Anyway here's another issue. It is not illegal to drive a car with no MOT or Tax to a pre booked MOT apointment at a garage. How does that one work?
Recently I sold a car without an MOT to someone who then drove it all the way to Hartlepool for an MOT, I thought that was stretching it a bit but apparenlty its legal.