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The number of people that used to say when pointing at the sidearm "Is that real?" The big guns were usually in the gun safe in the car until required. I think nowadays people are not shocked to see armed police because of exposure at transport hubs and abroad but because they're not everywhere they do moderate their behaviour. A drunk on a stag do walking past an armed cop suddenly sobers up a little when they spot the guns and then forgets to ask if they can wear your hat etc. Drunk ladies, in my experience, seem to be drawn to the firearms. In those cases it's best to relocate and remove yourself rather than the problem.
Would you say that the presence of armed police modifies behaviour anyway so there's less chance of more petty criminal acts taking place? I only wonder because even though there are quite a few places in London that always have an armed presence it's still quite shocking when you see armed rozzers, whereas in France you see Gendarm casually waving around guns everywhere so you just get used to it.