You can book the test online - the website tells you which centres can do each type of test.
Trailer test have to be done at HGV test centres, as they have the space for the reversing manoeuvre and the emergency stop.
The test itself should last about 90 minutes, with the driving portion of that a minimum of 50 minutes - the rest is taken up with the questions and manoeuvres.
The easiest way is to contact a local HGV/PCV driving school as they are likely to have (or know who does) an appropriate trailer for the test (it has to be a certain size and weight). You cannot just rock up with your own trailer.
Best bet would be to contact a driving school - the test isn't massively hard (I did my D1+E a little while ago), but you DO need some time to learn how to do things they way they like (particularly the hitch & unhitch - which has no relation to the real world at all). I reckon a day of training, and then the test on the next day. There are an awful lot of things to remember, and trying to cram in training & test in one day is one hell of a lot - and ultimately could just lead to you wasting money on a failure.
The reversing move is pretty easy, but again - very specific on where they want things to be positioned and how to do it - it's good to have a practice before you do it, and also to "learn" the trailer you'll be towing.
Best of luck.