NATS will send you where their business requirement needs you. Historically they’ve given trainee’s own preferences/circumstances very little consideration (i.e. none at all) It’s a great career but if you are thinking of NATS you really need to go in with the attitude that you can and will end up anywhere.
You could consider ANS at Gatwick? They are currently recruiting for trainees
Careers Gatwick Keep in mind they also provide ATC at Edinburgh, not sure if they have an open posting policy too. Be snappy though, applications close on Monday!