This is subject to change as the RTA is updated and amended.
Section 185 Road Traffic Act 1988 defines:
motor car, as motor vehicle - mechanically propelled vehicle.
Section 143 Road Traffic Act 1988 requires
Users of motor vehicles to be insured or secured against third-party risks.
In the case of Milstead v Sexton [1964] it was held that a motor vehicle whilst being towed requires an mot your vehicle and must be covered by Insurance.
Vehicle Excise and Registration Act 1994
Section 29 makes it an offence to use/keep a mechanically [propelled vehicle on a road.
But: under Schedule 2 (22) a motor vehicle proceedings to and return from a pre-arranged MOT is exempt from excise duty.
The car will also need an MOT & road tax unless it is going to a prebooked MOT test. Putting the car on a trailer negates these issues.