Q679: If I am driving someone else's car am I responsible for ensuring the car is legal?
Yes. Any driver who drives a vehicle, whether it belongs to them or not, has a responsibility to ensure that they are insured to drive the vehicle, that the vehicle is fully road legal, taxed and MOT'd.
If you are stopped by the police it is you as the driver who will face prosecution. Under certain circumstances the keeper may also be prosecuted.