There isn't a problem with "light" vehicles under 7.5 tons gross weight including loaded trailer,I tow my Jeep behind the Dodge, which is MOT'd and thats ok, its when you get into larger ie, over 7.5ton gross HGV stuff, the exemption from test and hgv licence only applies to pre '60 vehicles used privatley and unladen and can tow an unladen trailer.....mmmm spose you could always get a drawbar signals trailer converted into a caravan, which is ok to tow behind your exempt truck and load a vehicle inside it....
keep the curtains drawn though when travellng :-D