It is to do with urbanisation. Quite simply, the more people who live in cities the greater the amount of gun control.
It’s not just Britain and America. Switzerland, largely rural, has very little gun control, while America’s cities, as I understand it, tend to have plenty. I suspect one of the reasons for this is that in the cities you can have a reasonably effective police force. OK there’s the quip about “When seconds count the cops are only minutes away.” but better minutes than hours.
Also, I suspect politicians themselves are affected by this. In a city a politician finds himself surrounded by potential assassins, all of whom are nearby. “Best to disarm them”, he thinks. In less populated areas this is far less the case. It is perhaps no accident that high-rise New York City had gun control well before anywhere in the UK.