Not to stick my nose in this one, but those are semi quotes, and I use them all the time, and I'm Bx, NY, NY born n raised.
Which brings me to my main point, you did cite NYC - once synonymous with violence - being safer than London. It's also safer than any big city in America, and if you toss in per capita, than the interior West and whatever else...
Gun control (restrictions, pro active policing, gun buy back programs, social intervention, etc) has worked here. Yeah, yeah, Chiiiiiicago go! - apparantly the ONLY locale in the US mentioned in the 'opposing factions' fave stale argument, begs to differ...
And that's because it ain't NYC. Team NRA won't bring it up for obvious reasons, and Team NoGunFun curiously tends to not mention it as well (a sure bot giveaway)
The inverse of your point is true. New York IS safer than London because violent crime continues to dip at a rate surpassing and surprising expectations.