Well, after some considerable discussion in our mess room, my group are convinced a recovery vehicle doesn't require plating and testing in the case of towing a laden trailer because it is an exempt class of vehicle. The 'Goods vehicle built before 1960 and used unladen' part is irreleveant because it is not a goods vehicle, ie. it is not designed to carry a load (for the purposes of C&U a vehicle being lifted or towed is not a load).
I'm going to speak to a friend who used to be a chief tester and see what he thinks.
I remain open to other people's interpretations of the law but if I can satisfy myself that I'm legal I'll go ahead.