Google tells me 2,700 in Northern Ireland have authorization to carry firearms privately.

By comparison in my county in Washington state, there are 114,000 active concealed firearm permit holders out of a population of 2.3 million. And this is a liberal, fairly urbanized region.

We're talking ~50x the rate of people carrying firearms legally. Of course data on criminals carrying weapons is not so transparent, but it's suffice to say that American police are much more regularly encountering people with firearms.