There is something called LondonPass which you pay for upfront, then it gives free admission to various attractions.
5% Off voucher (though visiting the site today, I spotted they are doing a 10% off Valentines special still, though that ends today).
If visiting London this week, then you will need to pick up the pass from London Visitor Centre, No.1 Regent Street - having ordered it online.
LondonPass is quite costly but if you are in London for a few days then it is probably cheaper than individual admission to attractions. It also enables jumping the main admission queue.
Currently includes the following attractions:
Here are all the attractions you can visit for Free with a London Pass:
Apsley House
Banqueting House
Benjamin Franklin House
Britain at War Experience
British Music Experience
Cartoon Museum
Chelsea Cinema
Chelsea FC Stadium Tour
Chelsea Physic Garden
Chislehurst Caves
Churchill Museum & Cabinet War Rooms
City Cruises
The Courtauld Gallery
Curzon Mayfair Cinema
Curzon Soho Cinema
Eltham Palace
Estorick Collection of Modern Italian Art
Eton College
Fan Museum
Firepower Royal Artillery Museum
Foundling Museum
Guards Museum
Hampton Court Palace
Handel House Museum
Household Cavalry Museum
HMS Belfast
Jason's Canal Boat Trip
Jewel Tower
Kensington Palace & The Orangery
Kew Gardens
London Bicycle Tour Company
London Bridge Experience and London Tombs
London Canal Museum
London Motor Museum
London Legends Walk
London Transport Museum
London Wetland Centre
London Zoo
Lord's Cricket Ground
Monument
Museum of Brands, Packaging and Advertising
Museum of Rugby
National Gallery
National Theatre Backstage Tours
Pollocks Toy Museum
Queen's Gallery
QUEENS Ice & Bowl
Renoir Cinema
Royal Albert Hall
Royal Mews
Shakespeare's Globe Theatre
Tour & Exhibition
St Paul's Cathedral
Tate Britain
Tate Modern
Tower Bridge Exhibition
Tower of London
Wellington Arch
Wernher Collection at Ranger's House
Wimbledon Lawn Tennis Museum
Wimbledon Tour Experience
Windsor Castle
2 Day pass (without travel) is £53 adult, £40 child. Probably worth while if visiting 4+ attractions over that period.
TimeOut London includes information on various places to visit in London. Including Hidden Gardens, London Kids, Free London