I think Alasfoakus is taking about the centre of London (West End etc) which generally has many people around and therefore there is safety in numbers.
Of course you can quickly go from a busy street to a quiet street in seconds (Oxford St for example is usually very busy, but some of the side streets off Oxford St can be very quiet and dark).
I do not live in London any more but I gather some areas near the centre, like the back of Kings Cross station for exam[ple, can be very dodgy due to prostitutes and some unsavoury characters.
Of course London is huge and there are some of the more outliying areas that are dodgy. Brixton has a pretty poor reputation, for example, and there are others.
I did a search in Google for "Safety In London" and found this web site. There may be others:
http://www.allinlondon.co.uk/life/index.php?fi d=12