I can recall from my childhood that motor mowers needed to be registered if they were used on the public highway, including grass verges. The licence group for motor mowers was added automatically when you passed the car test.I have never even considered it, and certainly cannot think of any circumstance where it might be an issue!
Hire companies deliver and collect mini excavators, mini dumper trucks etc all the time, and no one has ever questioned the legality of them being moved from a site onto a trailer and vice-versa!