It does, but it is dot Gov, and frequently successive paragraphs appear to contradict each other.
I interpret "other aspects of vehicle use" to mean other than use as a trailer, but I am not a legal expert, and I don't know of any case law.
Cynically, I understand that the intent of HMG is to maximise the amount of revenue collected, so they would wish the vehicle that is legally a trailer to be taxed, but trailers don't have to be taxed.....
It would be displaying the registration of the vehicle towing it, too, which might be a problem with ANPR.....