Check your hand luggage at the airport--this will cost you a minimal fee for the day. You can pick it up when you come back. They will usually hold it until 11 pm.
Travel to the city. Taking a taxi is expensive and can take longer than public transportation due to traffic. The Heathrow Express train will get you into the center of town in 15 minutes but is a bit costly. If you have more than six hours to spend, take the subway. A ride on the Tube will take 45 minutes to an hour one way, depending on the time. Plan your day accordingly.
Check out the best shopping areas London has to offer! Oxford Street boasts a variety of department stores--Marks and Spencer's, Selfridges, H&M, Benetton and many womens' favorite: TopShop! Regent Street has higher-end shops.
Check out the open-air markets! Portobello Road has some of the most interesting antiques, while Camden market (take the Northern line on the Tube up north) has everything from knick-knacks to designer shoe and bag knock-offs to some of the best and cheapest Asian vendor food you'll ever taste.
Go to Knightsbridge and visit Harrod's. Pretend you're rich and wander through this giant luxury department store for hours! They have everything from $200 baby outfits to Pug-a-poo puppies in the pet department! Enjoy delicious freshly-baked bread and pastries in the food court, as well as fine chocolate and candy, various teas, sushi, seafood and fruit from around the world.
Visit the museums. Go to the Natural History Museum and Science Museum in South Kensington. See the mummies at the British Museum on Great Russell Street. They are all free. If you're willing to pay money to see some "culture", visit the London Planetarium and Madame Tussaud's, where you can see your favorite celebrities immortalized in wax, near Baker Street!
Talk a stroll through the park. Regent's Park in the north offers boat rides. St. James Park, near Buckingham Palace, has some of the most eclectic birds you'll see. Buy a loaf of the cheapest bread you can find at a supermarket in the city and feed the ducks and squirrels!
