Like any city, London has it's ok areas and not-so-ok areas. For instance, Hackney makes me nervous and I would not go there by myself. In fact, turned down a job interview because it was in Hackney.
I don't go out by myself at night if I can help it, but overall, I think a lot of it is just common sense - don't carry valuables if you can help it, keep tight hold of your bags and purses, keep your head down and keep moving. Works for me and I feel ok in London.