Considering its size and the great disparities in wealth, London is a remarkably safe city; it has one of the lowest murder rates in the developed world. Nevertheless, you should take the usual precautionary measures against pickpockets, who operate in crowded public places such as the Underground and major tourist attractions. At night, a bus or taxi can be a safer option than the Tube.
A major London hazard remains its traffic. Remember to look right before crossing its highly congested roads, and don't expect mercy from couriers or taxi drivers.