Not sure what the odds are now, but back in the mid-90s a qualified applicant (as in, 5 GCSE passes, within the age range, etc) had about a 1% of ending up as a valid ATCO. I don't what to put you off, Adz, but you MUST have a back-up plan. If they ask you at interview what your back-up is and you say "nothing!", you'll most likely be marked down. A better answer would be "studying [insert any subject you like] at college/uni and applying to NATS again in a year" or "taking a year off in Australia/Canada/NZ and then applying to NATS and to universities next year". One of my course had applied three times, and I applied twice before getting in.
It's always better to be doing something when applying for a job, even working at MacDonalds. Better though, from the perspective of showing you have potential, is to be doing something which leads to a career, and it needn't be in aviation. If you're washing Cessnas or sweeping the floor at a flying club on the side, even better.
I'm not in favour of spoonfeeding, so I'd say it's up to you to find local flying clubs and aircraft operators and make your own contacts. While you're at it, scour the shelves of bookshops for everything you can read on ATC, find the websites for NATS, CAA and AIS and any published information you can get your hands on. Visit ATC units! You have one ATC centre and two regional airports nearby, and all you need is a phone book and some confidence to arrange a visit.
Good luck!