Your qualifications aren't much good to you in the UK.
Unless you got accepted for a NATS Cadetship, to get a CAA licence you'd still have to undertake an "assesment for prior competence".
Thereafter the most credit you'd get against any of the ratings is 50%, so you'd have to do at least 50% of that course again.
If you got a NATS cadetship, you'd be doing the full course, but you wouldn't get a choice of whether you work at an airport or an area centre, you'd just be streamed for one or the other.
Be aware that some of the UKs largest employers (and I don't know if NATS are among them) often state (and are legally entitled to do so) that you must have "unrestricted right to work and to permanently reside in the UK".
Lastly, because I'm a cynical old fart who enjoys playing the devils advocate,
1) employment law or not, you'd have a tough time convincing any UK ATC employer that you are a better risk than any of the British applicants.
2)If you were an employer faced with spending many thousands of £s on training a prospective atco, you'd want a guarantee that the person you employed was going to stay with you for at least three years.
Many non NATS employers require trainees to sign bonding agreements (which despite what some may say, are enforcable and have been enforced),
could you commit yourself to that, or even convince an employer that you would be willing to stay?