As someone who spent most of their life in the UK, allow me to explain why you are
utterly wrong.
> There are likely a greater portion of unarmed criminals in the UK. Since their potential victims are also unarmed, that means that they are at the mercy of physically dominating criminals.
It's certainly true that most criminals in the UK are unarmed, but the "physically dominating" bit is way off the mark because most criminals are not physically dominating - anyone can be a criminal - the factors driving people towards crime have nothing to do with physical stature. This means that the majority of criminals are actually not particularly threatening, I have a friend who was mugged and simply picked up his assailant and threw him over a wall, another just laughed in the face of the teenager who threatened to mug him and walked off. Pepper spray and some knowledge of self defence will make you well prepared to handle the vast majority of criminals in the UK.
> Practically speaking, a person with a 6" knife can do far more damage to a person and have a higher likelihood of inflicting a mortal wound than someone with a .38 revolver.
First of all, knifes are also tightly controlled in the UK, though obviously smaller knifes are not particularly hard to come by. No doubt a skilful knife wielder can do a lot of damage to a person, but most criminals also are not skilful. At all. An inept gun wielder of any physical stature can effortlessly kill someone from yards away, in an instant. It's so easy, a toddler can do it. Also it's a lot harder to accidentally stab someone than to accidentally shoot them. Furthermore, those so inclined can (and do) learn how to fendoff a knife attack - you can't do that with a gun attack.
> my entire point is that more restrictions means that it's in the best interest of an armed criminal to obtain the most effective firearm possible.
That's completely backwards. You could hold up pretty much anywhere in the UK using a fake gun or an air rifle. There's absolutely no need for criminals to have actual weapons when their victims and the police too, are unarmed, because they pose no threat. Contrast this with the non-restrictive environment in the US where an unarmed or poorly armed criminal risks being shot by their victim, a responder, or the police. I live in the US now and my local ATM has an armed guard for crying out loud. That's an incredible incentive for criminals to turn up very well armed.
> rates don't really factor in to this thread
Oh but they do, because criminals with guns don't just wave them around for show: they use them. The per-capita homicide rate in the US is 5x higher than the UK and that difference is almost entirely composed of gun crime [1]. Take a moment to think about that.
So in conclusion, the U.K. is much, much safer because criminals don't have access to lethal weapons that are effortlessly easy to use and the statistics spell this out as clear as day.
[1] http://www.bbc.com/news/world-us-canada-34996604