I'll be in London and have jet lag so an evening out may be perfect! Any suggestions of plays or musicals welcome! Thank you-
http://www.theatremonkey.com/INFORMATIONBYSHOWTITLEAtoZ.htm#
You can look for yourself.
Trying to stay awake during a performance is bad value for money. But if you insist, The Play That Goes Wrong is so frenetically slapstick as to discourage nodding off.
If you must go to a play that night, pick something cheap as odds are you'll be nodding off before the end. I went to see a play the first night once and never again. I found myself nodding off and to this day, I can't remember much about it.
Agree that jet lag + play = 2 hour nap. However if you insist, head to the Leicester Square TKTS office for discounted tickets for a play that night. We saw The Play That Goes Wrong on our last trip and it was hilarious. It should keep you awake.
How early will you arrive, and will you have time for a substantial nap in your hotel room before heading to the theatre? As others have commented, you may have trouble staying awake through the performance if you're coming straight off a transatlantic flight.