Police have been routinely armed in Birmingham where there is a large gun problem among immigrant communities. Post-11th September you will now see armed police at places like airports.
Every police force has several elite firearms units that are called out to incidents involving guns - the policy is usually one of containment until they arrive.
The vast majority of gun crime doesn't affect the majority of the population, mainly taking place either within an ethnic group (so-called "black on black" shootings) or between rival gangs (usually black and asians). Thus arming police country-wide would serve no real purpose yet increase the risk.
Not to mention that, when polled, many police officers don't actually want to carry guns, reasoning that they can do a better job of 'community policing' without one.
It seems to work pretty well normally - most violent crimes are committed with knives and these are easily dealt with by a competent officer.
Just tragic events like this get through the net sometimes
My thoughts go to the family.