Among the smaller, quirkier attractions are the Hunterian Museum, whose skeletons and specimens trace the history of surgery and anatomical study. Or drop by the Bank of England Museum to learn how inflation is calculated, handle a gold bar and look at a collection of banker-bashing cartoons stretching back several centuries.
HAMPSTEAD HEATH
One of the best places to get a sense of the sheer scale of London is Parliament Hill, on north London's Hampstead Heath (confusingly, it's nowhere near the Houses of Parliament).
Tramp up the gentle path to the summit for a panoramic view that takes in the dome of St Paul's Cathedral, the giant Ferris wheel known as London Eye, the financial district's modern skyscrapers and the latest addition to an ever-changing city the 72-storey glass high-rise known as The Shard.
Then spend some time wandering the Heath, 790 acres of woods, grasslands and ponds that feels very far from the hubbub of the city. The neighborhoods on either side, Hampstead and Highgate, are both affluent, village-y enclaves full of highly desirable old houses and some good pubs. For a drink, try Hampstead's cozy Holly Bush or the 400-year-old Spaniards Inn - once the haunt of highwaymen, now treasured for its large beer garden.
AUCTION HOUSES
You probably can't afford to buy an Old Master or modern masterpiece from Christie's or Sotheby's, but the auction houses are still a thrifty art-lover's dream. Both regularly hold public exhibitions ahead of sales at their central London premises. The walls of the calm, airy rooms will be packed with art; there might be Rembrandts or Picassos, Francis Bacons or Damien Hirsts, all being given the once-over by prospective purchasers. Watching the buyers can be as much fun as looking at the art.
EAST END
If you want to see why London is known as the home of cutting-edge fashion, head to the city's trendy East End on a Sunday morning. Start at Columbia Road Flower Market. It's both a traditional street market, where Cockney vendors sell all sorts of plants and blooms, and a magnet for art students, hipsters and fashionistas. They turn the narrow street into a trend-spotters' paradise as they browse in the boutiques selling quirky crafts, clothes and furniture.
A short walk away, the area around Shoreditch High Street and Brick Lane holds more independent clothing stores, cafes and a large Sunday crafts-and-clothes market.
CEMETERIES
London's historic and atmospheric graveyards are tourist attractions in their own right, though the most famous, Highgate Cemetery, is not free. You'll have to pay a few pounds to wander the wooded paths and visit the graves of Karl Marx, novelist George Eliot, punk impresario Malcolm McLaren and many others.
Instead, visit Abney Park Cemetery in the scruffily fashionable Stoke Newington area. It's a splendidly spooky, overgrown graveyard full of crumbling monuments and a ruined chapel. William and Catherine Booth, founders of the Salvation Army, are buried here.
Right in the financial district in the city center is Bunhill Fields, which served as a burial ground for religious dissenters starting in the 17th century. Now it's a miniature oasis for lunching office workers, and home to the graves of "Robinson Crusoe" author Daniel Defoe and poet William Blake.