It might work, if the patrols of strapped rozzers are comprehensive enough to scare thugs to keep their pistols hidden.
Oh it'll scare people into keeping guns hidden alright - but only for as long as the armed deployments last and only in their immediate area. Like most crackdowns, all it will achieve is to move the problem around, more or less temporarily.
It would be better if law-abiding people were allowed to carry concealed weapons, as they are in that notoriously crime-ridden state Vermont. But this opinion is heretical, despite the fact that it rests on identical logic to that used to arm the police. Fanatical gun-haters like Ms McCartney have finally noticed this.
Best of all would be if people were free to carry weapons but felt no need to, as used to be the case in notoriously gun-ridden Edwardian Britain. For that to happen, armed criminals would have to fear the consequences of committing murder. But we refuse to hang murderers, so must instead impose the useless liberal alternative to the death penalty, gun control. Or rather, "law-abiding control", as that's the only people it affects.
I don't believe that concealed-carry laws would achieve anything other than more fights escalating into shoot-outs, frankly. I'm well aware that there are societies with such laws, very high rates of gun ownership and very low crime rates, but the reasons for that are in large measure social, cultural and economic, as are the reasons for some societies with high gun ownership and the rest being very violent. You are quite right to suggest that it's silly to blame guns for the actions of the people who fire them, but the actions of those people are conditioned by the societies in which they live. My (rather pessimistic) assessment of British society is that mass carrying of firearms would lead to them being used far more than they are now, and would not effect a significant reduction in crime.
I'm not at all convinced by your neat suggestion that gun control is an alternative to the death penalty. The motives for it are IMO far more complex than that. It goes without saying that I don't buy the argument that the death penalty is a deterrent either - but let's not go there...
Finally, from 1870 you had to have a licence to carry a firearm in the street, so it's not accurate to say that people were free to carry weapons in late Victorian/Edwardian times. Also, comparisons between then and now should be qualified with the fact that, although freely available, guns were considerably more expensive than they are now. Some criminals did carry and use them, but not usually the muggers and assorted other petty criminals, many of whose hands they'd almost certainly end up in today.