That's probably why they think Britain is very safe and calm- the bobbies don't have guns. OTOH, it's my opinion that it's actually less safe for that very reason. If the bobbies don't got gats, then only the gangstas do.
What you need to consider here is that there are basically two ways to acquire a firearm: 1. By bein a long-standing and respected member of a hunting or target shooting club. 2. Illegally.
Naturally, people in the first group account for a tiny minority of the population, and the sort of people attracted to such organisations aren't usually the type for committing violent crime. People in the second group will be pretty deep into crime over here to even be thinking of importing firearms. Keep in mind that most murders in Britain are through stabbing, and almost none through shootings. Your average crim on the street, even if he is a gang member, will be carrying a knife. The closest we get to "gang warfare" is a group from one gang stab a bloke from another gang.
Armed criminals will usually either be mooks who are given guns by their drugs-trade masters (eg to "defend" something important) or those who are paranoid and in over their heads. The police will usually know exactly who these people are before taking action.
If somebody is known or suspected to be armed, then the standard way to deal with them is with armed police. Usually there won't really be a fight. The mooks will shit themselves, drop their weapons and make themselves look harmless just in time to be arrested, or get shot. If it's somebody from the other categories (recent case was a bloke in the back of a taxi was stopped by armed police on suspicion of being armed. He panicked, shot one of the officers and was promptly totalled by the second officer. The first officer was unhurt because the round lodged in his radio. The man with the firearm had no importance whatsoever. In fact, all he was guilty of was illegal firearm posession, so he didn't need a firearm really, unless he thought somebody was after him. It is thought that he simply had one due to paranoia, which explains why he flipped out when the police caught him.) then most likely they'll either panic and attack, or see that they're in deep shit, and let themselves be arrested.
However, for everybody else, a policeman and his trusty baton will solve all problems.