These aren't facts.
The homicide rate in the UK is a quarter of that in the US.
List of countries by intentional homicide rate - Wikipedia, the free encyclopedia
And the US is not the worst in the world simply because there are tons of countries in much more advanced stages of disintegration where there is absolutely no control over guns or violence.
That said, the argument is not about the homicide and gun violence rates on their own, because those are affected by other factors than gun control. If you have powerful drug cartels warring with each other, the law may ban private gun ownership completely and that won't make much of a difference, they will find ways to get the guns. The argument is over:
1) Whether it is a good idea to have everyone armed allowing anyone who flips out and decides to gun down a dozen people because he sees no purpose to his life and this seems like a proper way to go out to actually carry it out. I will return to this after going over this first:
2) Whether it is a good idea to have such easy access to guns that kids on the streets can get their hands on them and actually engage in deadly turf war with each other. Which does greatly affect gang violence, BTW. Where I am from, the conditions after 1989 were ripe for the escalation of street violence because the same conditions that have created place like the South Side of Chicago developed there too. And indeed there was a segregation of neighborhoods, and drugs flooded the streets, and tons of kids are using them, yet there never was any violent street crime other than beatings and the occasional stabbing. Organized crime was responsible for a lot of shootings but almost nobody not involved in organized crime died in them. The same was true for most of Eastern Europe. And I think the fact that you can't get a gun that easily played a big role. There have been a number of suicides and some suicide-murders, BTW, but those have all been carried out by military of police personnel who do have guns. And when it has been a suicide-murder, it has been limited to the immediate members of the family - nobody has gone on a rampage shooting random people. That's true for the whole of Eastern Europe, BTW.
Which leads me to the second factor - social cohesion. What was not discussed even once in the month since Sandy Hook happened was that the reason people do these things in the US and they don't do them in many even more heavily armed places in the world (and gang members in the US who otherwise do a lot of crime do not do mass shootings) is that the US provides a unique environment of social alienation that drives people (predominantly young WHITE males, which is very telling) to such desperation with their life that they decide that the only way to bring some meaning to it is to do something like that and be remembered next to Charles Manson or someone else of the sort. Social alienation that is the direct result of the same socio-economic philosophy (ruthless unregulated capitalism and Ayn Rand-ian individualism) that the NRA in its current form is part of. That's a much bigger problem than gun control and if it can be solved, gun control would be a trivial issue after that.