Shayne, I think that there is a difference between what you are considering registration of a trailer, and what Clive is talking about.
In the UK commercially produced trailers need to have a Chassis plate detailing the manufacturer, ULW, MGW and a chassis number. What they do not need is their own registration mark (the proper name for the registration plate)
However, in much of Europe (and Australia) they are treated as separate vehicles, and therefore require registration with the equivalent of the DVLC (or whatever they are called this week) and get issued with their own registration mark, as well as undergoing annual or bi-annual (or only on change of ownership) inspections, and have to pay registration fees akin to the UK's VED.
Now what I do know is that since about 2007 trailers commercially built in the UK can only use dedicated trailer components (I wanted to get built a dual purpose canoe/kayak and mountain bike trailer with modules that could be swapped depending on what was being used, but the spring and shock absorbers wouldn't be suitable for both; I wanted to use Monroe Load Levellers but got told that as they were for a car they couldn't be used on a trailer), and I suspect that the home build stuff is coming into line with that.
Having a quick look at the
VCA website it also seems that the routes are very similar to cars; high volume Europe wide certification, low volume UK only, and Single Vehicle approval (one off vehicles/Ultra low volume)
Do I support registration and inspections for private trailers? Hell yep.... might stop the caravans falling over on the M5 every summer after their ancient tyres/suspension/chassis has let go once it's been vastly over loaded and under maintained! However, is it practicable? Not really... one day it will be but at the moment, not a chance...
On the subject of driving licences, it's been a bit of a cock-up from what I understand; IIRC the Germans have a much more sensible set up where the car licence holder can undertake one day of training and be allowed to tow... in the inevitable way the UK implemented the strictest proposal, whilst the others did the minimum...