If you would like to use your trailer in most existing EU counties, for business and commercial purposes and its gross weight is over 750kg and less than 35ookg, you will need to register your trailer with DVLA.

These regulations do not apply to trailers that are to be used abroad for personal use, such as camping, house moving, etc. and the trailer has a gross weight of under 3500kg.

You can register your trailer voluntarily, even if you do not intend to use it abroad and it is over 750kg gross and you only use it for personal travel.

A trailer registration plate can be purchased online at:
https://www.westerntowing.co.uk/product/trailer-registration-number-plate/
These plates are slightly smaller than a vehicle number plate so cannot be used on a car.