Bottom line: Police are trained in the use of restraint in both the United States and the UK, not in the use of force. They have it etched into their skulls in the academies. Giving them firearms does not change this. If anything it increases it, since that's one more thing they're trained to use with restraint.
And you're drawing an odd conclusion here Flip. Cops carrying guns do so for the same reason as the military. They are placed in situations where there is a very real possiblity they might need the gun to stay alive and accomplish their job. Firearms for them are a tool, something that they might need at some point. Simple statistics on the US and most other Western countries with armed police forces show that the vast majority of officers never fire their weapon outside of a shooting range. This is something that most people here in the US know, even if they don't actually acknowledge it. Even if a cop is pointing a gun at you, the odds are excellent you won't get shot.
Your presentation however seems to be extending into the reason that (unfortunately) some private citizens carry guns: because they like the power. Those kind of people are a danger to everyone around them. They exist, for the most part, because they don't really grasp what it means to use a firearm on another individual. Cops do know. It's training. It's practical experience. Even in the UK, police come in contact with people (dead or alive) who have been shot on a fairly regular basis. They know what pulling that trigger will do, they understand the consequences.
As to the belief that the criminals will arm themselves in response, and will start gunfights, that's ludcrious. Weapons have an irrational effect on people, but one rather different from what you're assuming. Consider: if threatened with a knife, most people will do what they are told even if it places them in severe danger, even if they outnumber the person(s) doing the threatening greatly, even if they could unquestionably subdue the threatener(s) and probably do so without sustaining any serious injury. Arguably criminals are less apt to be frightened then normal citizens, but certainly a firearm is a considerably more frightening weapon. A single man with a loaded pistol carrying only seven shots can hold a hundred people at bay. The saying that you do not argue with someone holding a gun is a much greater truism then you give it credit for. Many, many people with loaded firearms are arrested by the police without incident. It happens daily. Perhaps they got the weapon because the cops were armed (this is highly debateable; those arrested while carrying firearms almost always have them to protect themselves against other criminals, or to use them against the same or innocents), but when it comes right down to it, they are not willing to use their firearm against a police officer. The vast majority of criminals realize that there is no defense against the police save not being found, and the thought of shooting it out doesn't even enter their minds. Yet because the UK police themselves are mostly unarmed, then surely there are a few who see their advantage over the street cop and make use of it; a few that would not do so were they faced with a loaded weapon. To make matters worse, once you have injured/killed a cop, you can expect little in the way of leniancy (at the very least, your time while remanded to custody and awaiting trial is going to be a living hell). Those who see the advantage and make use of it, when confronted by armed officers from SO19 or some other group, may well keep fighting. There will always be a few who, from foolishness or insanity, insist on fighting the police no matter what, but they are not the only problem.
The main reason the UK gets away with an unarmed police force is because the criminals are largely unarmed too. But that's changing, has perhaps already changed as you've illustrated by your story about the gang. Such an event is not particularly common here in the US, and when it does happen, while there is alarm, people in nearby neighborhoods aren't told to get inside and lock their doors. They don't have to be, because the police can and will prevent anything from happening to them. They can do this because the police are armed, and it does not take too much in the way of firepower to bring a group of people to a screeching halt. Once that task is accomplished the situation is effectively over; whatever else happens is mere punctation of the point. Yet, as your story illustrates, the police in the UK, largely unarmed, at the least do not believe they are capable of the same thing: in point of fact they probably aren't.
As you say, arming the police in the UK in response to this one incident is a kneejerk reaction. But that does not prove the conclusion that they need to be armed unsound. At the very least, the time has come for the UK to start issuing bulletproof vests on a wide scale.
