Brits have a very different view of what is 'personal responsibility' and what is the government’s responsibility, or what is 'proper self-defense'. The English Bill of Rights (1689) was a 'right to arms guarantee' which has been castrated over the years, but was very influential to the framers of the US Bill Of Rights (The 2nd amendment giving every citizen the right to keep and bear arms). So way back when, there was not much difference in opinion.
It's not about assumption of responsibility at all. The UK population has always relied on the police for it's defence against crime. If you raise a hand against a burglar, chances are it's you going to prison, and they're going to successfully sue you for compensation. You cannot hit a criminal like you can in the US.
Brits are constantly bombarded by the Government and media with gun crime and how it could have been prevented if people had been prevented from owning guns. US citizens are portrayed as a bunch of gun loving psychopaths who can't understand that if they didn't have guns there wouldn't be gun crime, and a need to have guns to defend against it, all guns as portrayed as evil, every tradegy gets lots of coverage with the emphasis on how the lax US gun laws were to blame, they almost never report successful lawful use of firemarms for defence, genuine innocent sporting shooters in the UK always get blamed for any criminal incident and guns for the innocent made harder to get, and sporting shooters are made out of to be cruel pyschopaths who get enjoyment out of killing innocent animals / wildlife (not belying a need for pest control or wildlife balance) and are hated by the majority of the population. In my opinion, overall, the UK's Governments don't want their citizens holding firearms in any way shape or form, and engender a hatred towards guns, sporting owners and the US.
My personal take on it all, is the true path lies soemwhere between the US and UK position. In my opinion, the US has a lack of background checks (long guns), lax background checks (handguns) especially for mental health / previous violence, and inadequate security requirements - guns left in drawers, on bedsides etc. In my personal view these are the main issues that cause a lot of the US tragedies. Just my 2 cents though. The fact remains, in the UK there is no right to weapons for self defence and even punching a criminal can land you in a whole lot of trouble.