There is absolutely no indication that a generic arming of police in the UK would do anything to help them fight crime, and plenty that it reduces their ability fo form proper community liasion.
So long as there is no direct need for a wholesale arming of police in this couintry, it would be insane to do so.
Our police are gun armed only when it is necessary, and furthermore, by so restricting our gun use, the squads trained to do so are far more highly trained than the average gun-wielding cop in other countries, and the mis-use of such firearms is therefore massively reduced.
That our policemen don't need to be armed is still a point of pride in the UK. I think it is very difficult to quite get across just how much more rare gun crime is in Europe than in the States. There is nothing we actually need to match with such an policy.
As a point of reference, it is handguns that are illegal in the UK (beyond those things that are obviously illegal everywhere, like fully automatic assault rifles etc.). There is a shotgun in the cupboard downstairs where I live, though the amount of precautions my Dad has to go through to keep it are immense (it is for target shooting, btw).