No, the Police are armed enough where it matters (SO19, CNC etc.) and arming every regular Police Officer with a sidearm would be an prohibitively expensive and dangerous undertaking.
It's not just a simple matter of giving every person a gun, every Officer would have to be retrained extensively in the safe use and handling of a firearm, something that would cost a lot of money and something that not everyone would pass or want to do.
I'd imagine there would be large numbers of the Police who would refuse to carry a side-arm and use it on a person, it certainly wasn't something they joined the Police for, so if it was mandatory there would be a massive reduction in the numbers of Police due to people leaving.
Those vacancies may get filled, but probably only by people who had no desire to join the Police before (i.e. to actually serve and protect the community), but are suddenly very keen now that they get issued with a gun. They type of people who only join up because they want a gun and didn't/couldn't join the Army are probably the last people you want to issue a gun to.
Another issue is that if every Police Officer was armed, there would be a sudden influx of 140,000+ firearms on the streets of Britain. Not only would this make the criminals and opponents of the Police feel the need to be armed themselves, but a lot of those standard issue side-arms on the belts of Bobbys would make tempting targets for criminals. There would be a rise in attacks on Officers and fake 999 calls with the intention of luring the Police into ambushes* so they can steal their guns (*not "head 'em off at the pass" types of ambushes, but luring Officers into a small and confined flat with 4 people waiting to attack kind of ambush).
Not every existing Police Officer has the physical strength, hand-to-hand skills or mindset to defends themselves against multiple attackers in such a situation, but if we were to replace every Officer who isn't "hard enough" and lacks a "shoot-to-kill" killer instinct and reflexes, then that would be a great loss for the Community and Britain as a whole.
Jordi said:
It seems that everybody here is equating "armed" with "having a firearm" rather than "having a weapon".
That's because in the UK, "armed" in the context of the Police does mean "having a firearm".
The Armed Response Unit aren't just Police with Batons in a fast car, and when said Officers burst into a building and shout "ARMED POLICE!" they don't mean "I have a Baton too", they mean "I have a firearm and I will use it".