There are some UK region airports which employ ATC staff who are non-NATS. Only NATS staff are employed at ATC centres.
Some of the non-NATS ATC units pay for their own staff to be trained and some controllers pay for their own training course then find work. Only thing to do is to make contact with the Senior Controller/ Manager at whichever airport interests you and find out what are the possibilities.
Having worked both non-NATS and NATS I would say that non-NATS is a non-starter.... but I am certain that many will disagree.