To most British people, a knife (or sword or macheteetc) is a weapon, nothing more. Nobody uses proper knives (except a handful of bushcrafters, hunters, outdoorsman etc, and knife collectors of course) so they have lost all connection with practical use. The only time they see a folding knife or a machete is on the news when someone has been killed with one so gradually they have come to thhink of knives only as weapons.
It's interesting to note however that most stabbings in the UK involved cheap kitchen knives, not 'tactical' knives or machetes etc. Somehow, people have managed to ignore the fact that they use knives in the kitchen everyday, split them into two seperate worlds - evil knives that everyone else has, and my kitchen knives.
Then, years of media and government talk of 'too many people are carrying weapons' people have just been engrained with this idea that weapns are evil and need to be banned. It's genius really because now we have a situation where only outlaws and thugs carry weapons, so when someone like me calls for everyone to be able to, people immediately think everyone will end up like those thugs and outlaws.