For the first poster, NATS towers aren't always too keen to allow visitors unless they are already in the recruitment process, but still worth giving them a try. Otherwise try the non NATS towers.
For those going through the recruitment process and wanting a visit before stage 3, then it's quite easy to sort out. Either speak to HR for some contact numbers or have a look in the AIP (you can search on line for this under CAA documents) for your chosen airfield and you'll find the number for ATC. I'd recommend two if you can to get a broader picture and a better idea of what goes on.
Good luck!