The British police actually voted against routine arming of officers in the late 1990's.
Police at airports and nuclear installations are routinely armed with MP5's (semi-auto, I believe). Also, there are uniformed officeres with Armed Response Vehicles (squad cas with 2 officers and MP5's and probably 9mm sigs). They routinely patrol and assist in incidents involving guns. On top of that there is SO19, which is like a SWAT team. I'm sure there are plainclothed units who carry sidearms too, like the royal protection squad and probably drug squads etc.
The typical patrol officer has a nightstick (side handle now) and some forces have CS spray I think. Tasers are being evaluated.