I'm no lawyer, but I studied laws of contract for three years when I was a Clerk of Works.
I presume that parking regulations only apply to those vehicles which come within the Road Traffic Act - eg are registered, [thus have a logbook, tax, insurance]; and trailers probably come under the same regulations when connected to a vehicle and fitted with reflectors, lights etc.
It therefore follows that a "trailer" when not so connected is no longer a trailer and becomes a barrow or handcart, etc, and not liable, [except for obstruction, of course].
If it were liable, then so would be a perambulator, pushchair, wheelchair etc.
The only Caveat to all that is; bear in mind that policing and so-called "Traffic Management" nowadays is very little to do with upholding the law, and much to do with grabbing a £60/£80 fine, and getting a pat on the head from the Chief Const, [I think I've abbreviated that correctly], and a dog biscuit!
There - that's my piece!!
Baldeagle in Staffordshire