Chrisy08
I've not been to that college, but in view of the fact no one else has answered, I will give you a short, hopefully factually correct answer.
The 'international airports' as you call them Heathrow, Gatwick, Brizzle etc are controlled by NATS controllers - NATS has to bid for the contract to renew it whenever it comes up.
See
http://www.nats.co.uk for further airports that NATS controllers work at.
Traditionally, these 'NATS' airports were manned by controllers who have been trained at the college at Hurn (Bournemouth, but nothing to do with the airfield or tower there).
However there is a shortfall of qualified controllers all over and NATS do sometimes take on controllers who already hold a valid TWR/Gnd licence.
The course at Cwmbrawn will furnish you with a student licence which will enable you to apply for jobs where you will need to undergo further 'On the job training' to obtain your full licence.
There are several places where jobs are advertised - Flight magazine being one of them.
I am sure that the staff at Cwmbrawn will be more than happy to advise you if you call them - and I am equally sure that once you are on a course with them, they will give you advice on how to go about finding a position of employment.
Airports are run by a variety of diffeerent agencies, from private companies to local councils.
The trick is to get your student license - thats step one.
Then get a job and become valid. Once you have a few years experience under your belt you can look at moving to another airport if you wish.
You could always try to apply for NATS - though you are more likely statistically to be sent Area rather than App/Twr if you pass the training.
If you are hell bent on being a Twr controller, and paying for your own training, then e-mail or call the guys at Cwmbrawn - they will be more than happy to help you.