I lived in London for a semester. The "bobbies" are the nicest and most helpful people. This was in 2003, right before the Iraq war. I attended the anti-war rally to Hyde Park. Nearly two million people, and the cops were as calm and friendly as you can imagine, and not one of them had a gun.
The difference between police officers in America and Britain is that American cops look at the population as something that must be controlled, and therefore guns are necessary. The power struggle stems directly from the presence of the police officer's weapons, which intimidate the populace, no matter how necessary they are.
In Britain, the cops see themselves as public servants but still part of the general population. The number one job of a police officer in London is giving street directions to tourists. No joke.