In such situations it's possible to bring in special police units with guns; that doesn't mean you now have to equip every bobby with one. Thankfully in the UK regular police still don't carry a gun (except for NI, but that's historical), and, unsurprisingly, the number of people killed by police in orders of magnitude lower than the US. And the UK homicide rate is 4 times lower than the US, which proves that having more cops with guns does _not_ reduce violent crime.
If you want to point to a single factor as having / not having an effect between 2 groups you need to account for other factors. You could setup a statistical model.
So to be clear, the fact that policemen in the US/UK do/don’t carry guns and have higher/lower crime rate doesn’t prove anything on its own.
