The history of gun control here has always been of interest to me and it started long before WW2.
Control of weapons here started as early as the 1200s and really increased in strength from the 1600s. Gun licences have been a requirement since 1870. Pistols came under scrutiny and control just after 1900, with the 1689 bill of rights saying we had the right to own guns "as allowed by law" meaning that the law was always able to control gun ownership in England. Gun control that we would recognise with the Police and Home Office involved started as a result of two simultaneous cultural 'worries' - communism and the Irish. The Firearms Act 1920 was ostensibly to control the glut of weapons floating around after WW1 but the real intention was to try and frustrate the Irish Republicans from getting easy access to weapons.
We've been on a knee-jerk driven policy merry-go-round ever since the "Americanisation" of guns and gun culture worldwide. Honestly, if the USA behaved themselves properly we'd get a lot less grief here. There was an average of more than one mass shooting per day in the USA in 2025 and those sorts of statistics do tremendous harm to our sport here. Every time something happens here (Hungerford, Dunblane, Cumbria, Devon) we get something close to hysteria that we're on a trajectory towards American-style madness. We're not, but the global perception of guns and gun culture is heavily driven by the USA.