Hi Chris
At the moment you don't need any formal qualifications to be a dispatcher in the UK (I assume by dispatch you mean Turnaround Co-ordinator rather than the American version of a dispatcher, which is a very different job?) However the City and Guilds Aviation Studies qualifications would look good on your CV, and would teach you some of the basics, so I would suggest you do some research in that direction.
Once you have that, or even while you are studying, look at applying to airport handling agents as either check-in or loading staff, then work your way to dispatch from there. That seems to be one of the most common routes into the job these days.
I'll warn you now, the hours are awful and the money is crap, but in other ways it's probably the best job I've ever had. You're not stuck behind a desk and no two days are ever the same!
Hope this helps.