The official line from NATS is that they do not mandate an ATC unit visit, prior to final interview, or joining the company. However, in my own stage 3 interview (which was relatively recent), I was asked "Have you visited an ATC unit?" When I answered "no", the next question was "why not?". Read into that what you will. It will do you no harm, in fact it will look good.
Seeing as you are in the NATS interview process already, contacting NATS HR may be a start point. Not sure what they will or won't do but they may be able to at least get you a contact.
Another angle is simply getting the phone number for the ATC unit and giving them a ring. Look in the AIP (
link here). Every airport has its own section, and in the textual data PDF there will be a contact number for ATC. Just give them a call, explain your situation and ask... they can only say no!
2 considerations:
1) It will probably be infinitely easier to visit a unit where ATC is "landside" as it negates the need for security clearance, passes etc.
2) Just because you want to join NATS, doesn't mean you have to visit a NATS unit. (you may find less red tape elswhere!)