Do you want to go to a general destination or do you want to go to a "gay" destination?
For an easy weekend gay getaway from London, Brighton would be my first choice. It would even work well for a "down on Saturday, back on Sunday" visit. It's a big weekend party town and has a decent gay scene. However, many hotels require a min. 2 night booking on weekends. You can sometimes avoid this by using Travelocity or similar US websites.
For a bigger gay getaway from London, Manchester would be my choice. The city is very compact, has the largest per capita GLBT population in Europe, and is a lot of fun. Stay near the gay village and you can walk everywhere and never take a cab. Virgin Trains has great service from London Euston with advance fares as low as 11GBP ow when you can snag them. You can also fly ow for as low as $52 all in between LHR/LGW and MAN.