That's a very sweeping statement! Britain has a far more violent history than the US, having participated as an ally or an enemy in most of the wars the USA has fought, and very many more besides. Most of the old European states have similar histories to Britain. We have fought between ourselves, and very notably, created empires through military and economic might, fought over them and with their people for centuries.
No doubt you could come up with many egregious examples of aggressive foreign policy by the US, but I very much doubt that they exceed foreign atrocities of their Old World progenitors.
Nevertheless, American gun culture is clearly a thing. Rightly or wrongly, some Americans see the right to carry a gun as important. And I can see the point. America is big. If you live in an East Coast metropolis, it doesn't feel much different to anywhere in Europe. A policeman can be on the scene just as quickly in Boston as in Douglas, probably. But if you happen to live in the South Western US for example, on a farm where anywhere is a few hundred miles away across empty scrub, then having a gun in the house probably feels quite reassuring.
I do think the whole Second Amendment/NRA libertarian 'right to bear arms' is a nonsense, though, in a democratic state. I think the second amendment, having been written not long after the War of Independence and in the absence of a standing American army, was intended to facilitate the raising of militias: "A well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed." Take out that first and last comma, and the meaning is clearer.
Rather than being a right per se, firearms ownership ought to be regulated along the same lines as in the UK, where you have to show that you need a gun for genuine sporting or practical purposes. The type of weapon, and particularly the capacity for rapid firing of multiple rounds has to be limited, as it is here.