London's homicide rate is (roughly, depending on which source you use and year you take) about one-fifth of the average US homicide rate; you are safer in London than in almost anywhere in the US.
13 per million per year in London. 60 per million per year in New York.
That's an 0.006% chance of getting murdered killed in NY every year.
And that doesn't account for (a) putting yourself in a good position to get killed like being a gang member and (b) the aggregate reduction in risk by only travelling there.