Well, dispatchers in the UK are more commonly known as operations controllers (or some variation). There is no UK licence as such but plenty of training courses related to it.
It's best to start out as an ops assistant for the experience, and to see if you like it. The pay is crap at this stage.
I'm out of the UK loop right now, but I understand DHL at East Mids might be worth a shot if you fancy cargo.
At controller level the salary should be in the 20s and it can be advantageous to gain an FAA dispatcher's licence, this will give you the edge in job interviews and is a very interesting and hard 6 week course in the USA (see
www.dispatcher.org).
As for the job itself, it varies by company, but mainly consists of flight planning with a computer system such as Jeppesen's, flight following (tracking arrival/departure times), weather briefing, general organising and rearranging when it all goes wrong, and sometimes crewing.
If you're lucky you'll never be bored.
M