I found in New York the safety factor came from the absolute plethora of visible Police presence, in London you'll be lucky to see one roaming the streets.
That would mean the 'opportunist' in London will have more chance and temptation in London.
That being said i am fairly well travelled and have never really felt at risk anywhere, except Categena in Spain, where a chap started following me and 'er, until I stopped just around a corner and waited for him, as soon as he realised he bolted. Although I think the camera was the attraction, not the watch.
I think realistically the vast majority of places are ostensibly safe. If you move in criminal circles, expect criminality, if you move in civil circles expect civility. The only real threat is the opportunist, the only defence from them is vigilance.