The UK did take some action after theirs; after Hungerford, all semi-automatic rifles (centre-ammunition) and shotguns taking four or more rounds were banned, and after Dunblane all cartridge ammunition handguns were banned within Great Britain (except .22 single-shot, which were then banned about 5 years later).

The most recent UK shooting of note, Derrick Bird, used a double-barrelled sawn-off shotgun and a .22 (bolt-action) rifle. Would it have been worse if he'd had handguns and semi-automatic rifles? We'll never know, but he did try to acquire another firearm mid-rampage so he clearly felt like he needed more firepower.