The UK police force has always been the envy of the rest of the world, it's a model that many have studied and attempted to implement elsewhere. It's a tiered system with the humble beat bobby at the base and many levels all the way up to flying squads and highly trained and well equipped tactical armed response units. It's a classic case of what you see isn't necessarily what you'll get, if a beat officer requests tactical response it's on the scene in less than a couple of minutes. The beauty of the system is you still have police that interact with the public, they help old ladies across the road and they cuddle babies but not far behind that public-friendly exterior there are teeth, the criminals know it and the beat bobbies rely on it.
How is it better to arm the beat bobbies and lose that interaction with the public? Look at the police in other countries like the US, it's an us and them mentality and I don't mean between the police and the criminals, I mean between the police and the rest of the population.