In 2003 I sent a letter to the ATC manager at Manchester requesting a visit, which was granted. In the letter I explained why I was interested and why Manchester specifically.
I brought my passport as ID and had to be escorted at all times, but there was no actual security to go through, just a number of ID activated and coded doors to prevent unauthorised access.
IIRC I simply sent the letter to the 'Head of ATC'/'ATC manager' or something similar using the airports address; I'd imagine a similar method would work elsewhere.