Re category B with licence after 1997.

You won't find a normal Car / Trailer /Loaded vehicle combination that will comply with the 3500kg rule.

The trailer and loaded vehicle can't weigh more than the tow car.
So the moment you put a normal car on a trailer you're overweight for the licence class.
You may just get in with a stripped out track car on a lightweight trailer.

Most cars aren't rated for towing a car of the same weight let alone a trailer as well.
You need to be in a 4x4 to get a good towing weight, then you've little weight capacity left.

From https://www.gov.uk/old-driving-licence-categories
Licences issued between January 1997 and 14 October 2012

B. Vehicles up to 3,500kg Maximum Authorised Mass (MAM) and up to 8 passenger seats with trailer up to 750kg; trailers over 750kg if combined weight of vehicle and trailer isn’t over 3,500kg and the fully-loaded trailer doesn’t weigh more than the unladen vehicle