I've been living in central London (zone 1) for 3 years now and never had any issue (nor my partner, nor anybody I know). It might also be due to the area being

I've been living in central London (zone 1) for 3 years now and never had any issue (nor my partner, nor anybody I know). It might also be due to the area being touristy or not. I remember a crime map (I can't find out this link anymore...) showing that the side of London bridge which faces Tower Bridge had a high crime rate whereas the other side was absolutely safe. So if you want to cross London Bridge without taking a picture of Tower Bridge, pick the correct side :) London is a big city though. As most big cities, I would never expect it to be totally safe.