If you are as tall as you say you are then I can see ergonomic problems. However if NATS have offerred you a job then I think legally they have to comply. If you were applying to fly as a pilot then you would be too tall. The only problem that I can see is that you're height would make you too tall to see the radar screen, i.e. you're head would be too high. This is not your problem, it is a problem for NATS and you should not be discriminated for your height.
Where is the Flying Lawyer for advice.
If you do get the course then please do area control as we still need control towers.