This appears in the AIP for Manchester: 0161-499 5336 (Airport Watch Manager). Now whether that is the ATC Manager I don't know but you could try. If it's the wrong department I'm sure they could help. Alternatively, telephone Manchester Airport and ask for ATC.
I don't know what your motive is for visiting but it's often very difficult nowadays to visit an ATC unit unless you are a pilot ot ATCO.