Having no MOT doesn't make your car not roadworthy.

You can drive the car up until the minute before your MOT expires, in the exact same condition as the minute after.

This is why your allowed to drive there in the thinking your car is in a roadworth state, if you crashed on the way and it proved to be unroadworth there might be a problem.

Driving with no MOT isn't a points offence, just a fine.