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Apparently its not officially a requirement to visit a NATS facility prior to stage 3, however I would say it is still definitely advisable. At interview they will be looking for you to demonstrate motivation for the job, this will be hard to show if you don't have quite a thorough understanding of what the day to day job entails (how can you show that you are motivated to do a job if you don't fully understand what that job entails?) and the best way to understand this is to go and see a real facility at work and talk to the ATCOs there.
I visited Southampton tower after my stage 1 and found this really helpful. To arrange this I contacted the airport help desk and got the number for the tower's admin office. Once I'd explained why I wanted to visit everyone I spoke to was really happy to help and it was a very informative and eye opening day.
I'm also visiting Heathrow tower (tomorrow!!), I arranged this in an alternative manner (on advice from the people I met at Southampton) - by getting contact details for the relevant personnel at Heathrow from NATS HR. (note: don't try asking HR to arrange a visit for you, apparently they aren't very receptive to this.... but if you exlpain that you want to arrange a visit and just ask who you should contact about it they seem more than happy to help).