This article is from the Theatre FAQ, by aku@leland.Stanford.EDU (Andrew Chia-Tso Ku) with numerous contributions by others.
I maintain another document, The London Stage Gazette, which is
currently being updated monthly. It lists what's playing at all West
End theatres, the RNT, the RSC, and selected Fringe theatres, with box
office phone numbers and in some cases capsule reviews. It also
reports news on upcoming productions.
The latest version of The London Stage Gazette is posted to the Usenet
group rec.arts.theatre.misc. It can also be found on the World Wide
Web at "http://www.tiac.net/users/davidf/london.html" as well as the
London Home Page at "http://www.cs.ucl.ac.uk/misc/uk/london.html".
Finally, you can also get it by e-mail by sending your request to
firstname.lastname@example.org. I also have a mailing list which is sent the latest
version every month (as well as new versions of this document when
major changes occur); if you would like to be added send mail to the
same address (makes sure you specify whether you want to be added to
the list or just want the latest update).
In London, the weekly magazines TIME OUT and WHAT'S ON have complete
theatre listings, including all the Fringe theatres not covered in my
listing -- I always pick up the latest issues in the airport when I
arrive in England. They can occasionally be found in larger newsstands
in the States; in Boston TIME OUT can usually be found at both Out Of
Town News in Harvard Square and the main Tower Records on Newbury
Street. Another thing to pick up once you are in London is the Theatre
Guide, a free brochure put out bi-weekly by the Society of West End
Theatre and available at most theatre box offices.
London newspapers are also a good source for current listings; many of
them include information on ticket availability so you can check which
shows are selling out. Again, in the Boston area you can find London
papers at Out Of Town News.
In the States, the monthly newsletter London Theatre News reviews
recent productions and has a listing of West End theatres. The only
drawback is that it often doesn't review shows in time to help with
advanced planning (and the reviews are not always worthwhile in any
case). For subscription information, write London Theatre News, 12 E.
86th Street, Suite 620, New York, NY 10028, or call 1-800-779-0077.