London is a pretty safe place to visit and that includes travelling on London Underground (the Tube) or bus.
But be aware of the highly skillful pickpockets operating in all crowded places, especially Oxford Street, bars, pubs and the Tube.
Sometimes they operate on their own and sometimes in groups, surrounding and manipulating you.
Always keep your valuables out of view and within your field of vision and don't carry all your cash and cards in just one place.
Any theft or loss must be reported to the police if you want to claim on your insurance.
Here are some good web links on how to protect yourself:
http://travel.howstuffworks.com/pickpocket.htm
http://www.met.police.uk/tourist
http://www.met.police.uk/youth/street_safety.htm