Go window shopping in Covent Garden: plenty of things to see around there including some brilliant Street Theatre acts
Organise dinner/lunch in advance by booking restaurants on TopTable.co.uk: you can often get up to 50% off if you book up to a week in advance.
Go to a West End Theatre for cheap by buying the tickets on the day you want to see it from Leicester Square, but don't be picky about which play you want to see. The most popular ones are often still very expensive.
Go to a fringe theatre: Hampstead Theatre plays are usually brilliant, but there are some other good, cheap ones all around London
Go to a Museum: most are free, including the Natural history (the best by far), the Science and the Tate. All very good.
Go to a Bonfire Night party - all around London the firework displays on the Weekend of 5th November are usually amazing. The weekend after is when the Lord Mayor celebrations are held in central London too. Also very good.
Go to Camden Market - it's great fun and there's always something to see
Watch a tv show being recorded. There are so many you'll definitely find one to suit your tastes! TV Recordings
Stroll along the Thames for some beautiful London sites
Go to Regents Park, Hyde Park or Hampstead Heath for beautiful views
~george