My VFR flight guide gives telephone numbers for NATS (the company supplying ATC services):
Luton - 01582 395029 or 395299 (switchboard 405100)
Oh dear, your VFR FG is out of date then...
Call NATS Luton on 01582 395229/395230 (NATS Administration) and ask to arrange a visit.
Plan it only for 'office hours' so there's someone to host your visit.
You'll need photo ID as although like Stansted, the Tower is landside, as with Stansted it's within a controlled access area.
