Join the WikiGroundlings for a meetup (or multiple meetups!) at Shakespeare's Globe, an exact replica of the historical theatre, and get some tickets in "The Yard" for only £5 - ie standing-room like the Groundlings from Shakespeare's day.
Stage and galleries
Some times that are available:
Tues - Anthony and Cleopatra 2pm (though this may not be ideal for the jetlaggers!)
Wed - Anthony and Cleopatra 7:30pm
Thurs - King Lear 7:30pm
Sun - Holy Warriors 6:30pm (a contemporary play by David Eldridge that draws on Elizabethan dramatic methods. Trekkies might be interested to know that Alexander Siddig plays Saladin)
This experience involves a lot of standing among the proletariat, but also gets you a lot of cultural and historical bang for your money.
Tickets can be purchased here for £5 - remember that "The Yard" is where we're going, and this means you'll have to be comfortable standing for a couple of hours during the performance.