"The difference is that there's really one use for guns (especially in the UK which is really too densely populated for hunting with guns, except shotguns*, to be a thing), which is killing people."
There's competition shooting for a start. Post-Dunblane the ban lead to the shooting contingent of the UK Olympic team having to train abroad. And yet smarmer-in-chief Blair had his photo-opportunity with the team. I was surprised that those affected didn't boycott him.
The trouble with urgent legislation in response to something like this is that it's not well thought out and liable to err on the side of being too all-embracing or nigh on impossible to enforce. The pit-bull legislation is an example of the latter.
*I believe deer stalking uses rifles. There are large portions of the UK less densely populated than those you're familiar with.