Seems to have been a very quiet introduction of this one.

All trailers >750kg need to be registered for travel in Europe. It used to just be commercial trailers, but that's no longer the case.

The DVLA site is a mess, with it saying you need one, then you go through an (outdated) wizard that says you don't, but will let you if you insist.

Text here - https://www.gov.uk/guidance/trailer-registration

Useful video here -

It only costs 26 + the cost of the physical plate.