Just a few numbers:
Third, license. You only need to acquire your B+E part of the license (if you don't already have it) if the gross train weight of the outfit (car, fluids, trailer, YOU) exceeds 3.5 tonnes. You can legally tow a caravan/braked trailer over 750kg as long as the outfit weighs less than 3.5 tonnes.
... and very importantly the MAM of the trailer must not exceed the unladen weight of the towing vehicle. This will actually rule out most car transporter trailer / towing vehicle combinations.