I'm not from the UK, but what I can say is that ATCOs, like a good percentage of private and commercial pilots, are certainly no jet fighter pilots. My experience is that while medical requirements seem strict at first reading, there are many exceptions to the rule (like if you fail the hearing test, you can pass if you simply hear a low-level speech from a medium distance), and most doctors will do whatever they can to pass you, and they will seek even more possible exceptions when you are already a licence holder. However, providing false information might constitute a breach of law that will eliminate you as a candidate (here we have to provide a statement from a court we have a free criminal record).