Assuming it's your wife who wants the job, as an area ATCO, she could only work for National Air Traffic Services (NATS) in the UK.
She would have to undergo an APC (Assessment fo Prior Competence) to assess her current skill an competence levels, after which the UK CAA would decide what futher training she would have to retake.
Unfortunately NATS Management have a reputation for being particularly obstructive when it comes to accepting staff who have not been trained by them.
I know of a number of individuals who have completed extensive training at CAA approved training establishments in the UK to get various ratings, yet when they apply to NATS they are told they have to do all their training again to get the same ratings.
There's no legal reason why your wife shouldn't work in the UK, but the process is completely unreasonable and it seems unlikely that she'd tolerate it.
If you both want a change of scene I'd apply to Eurocontrol, much better terms and conditions and probably a better employer.