The problem is escalation: we are our police then criminals will have to start arming themselves, and they essentially enter an arms race (maybe a bit of an exaggeration, but the point still stands).
The reason our gun crime is low is because criminals don't need to use guns - they're expensive and difficult to get hold of, so the only reason they'd need them is if they are serious or if the police all had guns.
I feel safe knowing that the police in this country don't need guns yet, it makes us feel just a bit more civilised knowing that our crime isn't that bad yet. We do have a lot of knife crime, but the police are equipped to deal with that. Gun crime in this country is no where near the level seen in other countries, partly due to the difficulty of getting guns and partly because, if the police don't use them, criminals see them as an expensive item they just don't need.
And while armed police work well in America, you guys have supermarkets selling guns - of course your police need them. I will never understand why you feel safe with armed police, because the reason they're armed is because the average criminal is armed as well. That's a terrifying society (no offence, I just find the idea that anyone can buy a gun regardless of whether they are a responsible person to be rather scary).
I say keep the police unarmed because arming them will only lead to an 'arms race' between them and the criminals, helping no one.
I sleep relatively well at night not because I know the police don't carry guns, but because I know they don't NEED to carry guns.
Also, our crime rates may be fairly high but not necessarily as bad a the media will have you believe: http://www.homeoffice.gov.uk/publications/science-research-statistics/research-statistics/crime-research/hosb0611/hosb0611?view=Binary