The UK is a society where violent crime is pretty uncommon. The homicide rate in the UK was 1.0 per 100,000 population in 2023. That has been broadly trending downwards in recent decades, after rising during the late 20th century and hitting a peak at c1.8 per 100,000 in 2003. The US is a much more violent society: their homicide rate is around 6.4 per 100,000 population.
Killers are always going to find weapons - if you ban guns they'll find knives, if you ban knives they'll kill with something else. One difference is that a killer on a knife rampage is going to kill a lot fewer people before they're stopped than a killer with a gun. I guess killing with a knife is a more 'involved' act than just pointing a gun and clicking the trigger, so the bar for someone stabbing with a knife is probably a bit higher than killing from several metres away with a gun.
But part of it is a societal thing - my hunch is that (in relative terms) society in the UK and most other rich Western liberal democracies just instills in people an instinctively higher value on human life. You see it in US exceptionalism in use of the death penalty, the frequency of police killings, etc. I don't want to exaggerate the difference - the US still has far fewer murders than Colombia or South Africa or Brazil - but there are other Western countries like Canada or Finland where guns are still pretty widely owned (albeit not quite to the extent of the US) that don't have the same problem of violence as the US.
The homicide rate in the US is about 6-7 times that in the UK per 100,000 population. I'd take our situation any day of the week.
Last time I looked into this properly, knife crime in the US was actually roughly the same frequency as that in the UK. The difference is that knife-based murders stand out in the UK, whereas in the US nobody pays attention because the problem is dwarfed by the much greater problem of rampant gun crime.