In the UK, the situation with the police is fairly straightforward.
The majority of police, in prosecuting their role, do not need a gun. Most use protective clothing and carry preventative weapons like truncheons and mace. As they're unlikely to come across guns or similar day to day, their use as a deterrent or protection is minimal.
Where they do believe they require guns to prosecute their role, they carry them. I work in London quite close to the Old Bailey criminal courts and there are regularly officers with automatic weaponry on duty.
This approach is fairly pragmatic and mostly effective. I'm sure, if there was good reason to believe that either they or the public would be much better protected, if substantially more officers carried guns, then that debate would occur.
For the general population, it is possible to get a gun license but it's much harder than in many countries. As there's not much debate on the topic, it's hard to gauge a general view but I would argue that, as there hasn't been much violence where an armed public would have make a material difference, there's not much call to change the status quo.
There's very little gun violence in the UK, 20-30 fatalities a year. Terrorists currently seem to be mostly suicide bombers or drivers. The only case that I can think of recently, where an armed populace would have made a significant difference, is with the London Bridge incident. It's conceivable that more incidents like this could sway opinion.
One final point. Gun crime in the US is a fairly common talking point in the UK. I would argue that a common view in the UK is that the US has lost the ability to control guns, even if they wanted to, and that there is endemic gun violence. Whether this is true or not (I'm no expert) this view definitely dampens any enthusiasm for loosening our gun laws. I'd also argue that, of all countries, we feel that we have the propensity to be quite like the US and this is one area we do not wish to follow.