When you fly into Heathrow or London City, buy an Oyster card for travelling on the tube network and buses which can be purchased at the underground station at both airports. You can top it up at any station or newsagent and it is much cheaper than buying tickets. At the end of each day, the computer works out the cheapest fare and then changes the balance on your card accordingly. You will need enough money for a day's worth of travel though and you must 'touch in and touch out' when you enter and exit the station or you pay a higher amount. The cards don't expire either, so it's worth keeping (unless you never expect to return to London). I have had mine for several years.