In one of the statistics years ago it said that most muggings happened in Westminster. Loads of wealthy people, hence loads to steal.
Sometimes you have to be more careful in the wealthy posh parts than in the run down shoddy parts.
I never experienced anything bad, but a friend of mine had her mobile stolen out of her hand whilst she was walking and talking on it. Luckily that's the extent of bad things I know of personally.
I am actually baffled by people (regardless whether they're born into it or not) who are rich and flaunt it so openly, Rolex watch (gold preferably), Hermes bag (and accessories), recognizable shoes (Hermes, Blahnik etc), recognizable lables and logos from head to toe and I don't get it at all. It's like you're advertizing that you have money.
The world shoudln't be this way, but it is and I think people who dress so much in logos and well-known models are blatantly asking for trouble.