I am 18, just finished A-levels and will pretty much do whatever is going!
As Heathrow Director said, if you're 18 then why not apply to NATS for trainee ATCO? You've got 3 attempts, so what've you got to lose?
It would probably be more worthwhile and productive to apply to NATS, go through selection and just visit Swanwick (and other units if you felt necessary) rather than attempting to get work experience.
I just dont know who to contact
Try the phone book, or look on the NATS website - perhaps HR can provide you with the details you require?