There is no specific law about driving a vehicle without doors otherwise there would be issues with driving vehicles such as Beach Buggies, some Land Rovers (the old ones) and even tractors on the road. Then you have cars such as the Ariel Atom, Caterhams, Morgans and the like which don’t have doors.
But what you might come up against is the old hot potatoe of a copper being subjective and in his/her opinion quoting “Driving a vehicle in a dangerous condition” which covers safety issues to the occupants of the vehicle as well as individuals who may be affected.
If the door is actually missing and the occupants are belted in properly, I personally don’t see a problem.