Firstly, Luton is not an ATC Center - it's just a tower facility. Approach Control for Luton is carried out at West Drayton. Towers are usually cramped and space for visitors is limited.
Secondly your profile makes no mention of what you do so what does "jumping ship" mean? If you are a pilot, or have serious aviation connections it would not be difficult to arrange a visit to an ATC Centre - typically Swanwick, as had been suggested, or Terminal Control at West Drayton. Telephone the Watch Manager and explain the situation. If it's not too busy you may be lucky.