Yes they can. As I said, my new car has been given its registration mark already and I don’t pick it up until next Thursday.
If they have already registered the car, I am not sure if they can de-register it so you will either have to accept the 74 plate (which I would not do) or cancel the order and possibly go elsewhere.
Please can I ask what car you have ordered and are you prepared to accept the 74 plate or cancel the car?