I think that cities like London and New York only have the edge that they do because people come from all over, drawn by the fact that people before them have gone there to reinvent themselves and, in some way, make these places their own.
I'd say that there are probably more quintessential Londoners that are actually from London than there are quintessential New Yorkers that are actually from New York, perhaps due to the size of the US vs the size of the UK and the fact that there are far fewer cities in the US that can compete with New York as a source of art, culture and business. The concept is probably also less controversial in New York since it has always been an immigrant city (I saw a stat a little while ago that indicated that something like 40% of the population is non-US born).