It's indeed unfortunate that this impression has taken root in the U.S. as widely as seems to be the case. There seems to be little that those of us who know better can say in response which won't be summarily dismissed. Illustrate with personal anecdote, and we're accused of burying our heads in the sand, ignoring the reality around us, being blind to what's happening elsewhere than in our little safe enclave etc. etc. Respond with statistics or explanation of the law, and we're accused of hiding behind generalisation and abstraction, selectivity in the choice of statistics or even of quoting questionable evidence etc etc. In truth, I suspect that the only way anybody who holds this view might be convinced is by spending time here - and by that I mean a substantial period of time, not the snapshot observations of a tourist.
...but here's my personal experience, anyway. I've lived in England nearly 70 years now, not a particularly sheltered life, in many different areas (north, west midlands, south, southwest), in big cities, medium-sized towns, and in the countryside.
During those neat 70 years, have I ever experienced or felt in imminent threat of physical violence of any kind?
No.
Have any of my immediate family or friends ever been subject to or threatened by physical violence?
Not that I'm aware of.
Has a violent incident ever taken place within the near neighborhood of my home?
Not that I can recollect, or at least not affecting anybody I have known personally, even if only by sight.
Have I ever felt that owning a handgun might be desirable or useful?
No.
Has any of my family, including past generations, ever owned a handgun, even when there was no legal obstacle to doing so?
Not that I'm aware of.
Do I know anybody who owns a gun of any kind?
Plenty. All shotguns or a variety of sporting rifles. All owned for farming or sporting purposes. All owned without interruption through the various stages of gun control legislation.
Have any of these ever expressed to me a wish to hold other kinds of gun, including handguns, if it were legal to do so?
No, although the subject has occasionally been discussed in my presence when gun crime happens to be in the news.
And yet I see equal or greater condemnation of our gun rights in America from Britain, even though many of us can match what you wrote, outside of not owning guns.
Gun violence in the US is likely much like gun violence in Britain, it is in the big cities, by criminals against criminals. It is only of concern when criminals decide to prey on honest citizens, and that is where the difference lies.
The United States is fourth in land area of nations in the world, just slightly smaller than China and Canada. The UK is 80th, with just 93,800 square miles for 63 million people at a density of 673 people per square mile.
While the US has 315m people, they are far more spread out, with a population density of 89 people per square mile. And since most people live in much higher density on the borders, much of the interior is mostly empty.
This difference in area matters, because both the US and UK have around 300 police officers for every 100,000 people. And the US police are responsible for seven times the area.