As a gun owner in one of the countries that prides itself on strong gun laws. I'd say that the US model is not the problem, the UK model is no better.
Crime is the issue, gun crime is not.
Some people will sell out all freedom for the hope and illusion of safety, others accept there is a price for all things, sometimes the price is horribly high, no one wants to pay it. But we do, because the lie of safety is not worth the price.
I'm not going to say there isn't room for both arguments, or insist my view is right. I would say, do some honest research, real, open, fair and apples to apples reseach. I was one of the anti gun people, until I spent some time getting to know the arguments. I believe that an honest apraisal of things like CCP's will highlight that the gun laws proposed are unlikely to help, and really achieve little.
Look at Canadian long gun registry that is being scrapped, Australia's registry that can't even tell how many guns are in the country, let alone the illegal ones. Criminals in both countries have never had a crime solved against them with a registry and honest owners are made criminals by procedural misunderstandings and tiny obscure legalities.
Gun control has in my view failed, 14th cent. technology can't be unlearned. And banning drinking didn't work. So why would you continue to try failed controls. Stopping crime is far harder than banning a particular thing -- always has been.