instead of the old style britich copper who would actually chase criminals and have a chat your average joe.
It varies by location, by individual police force. Which it probably should as different communities require different styles of policing because they contain different kinds of people.
In York, for example, police would stop and caution cyclists without lights, and serve notices on cyclists who ran red lights. Police were present as regular street patrols, usually in twos of one male and one female. Trouble in the city centre received an immediate response from one or two vans but always in line with the (usually drunken) disturbance. There was a real sense that the York police were present, interested and active and that their response was proportional.
In Eastleigh, I've seen a lesser on-street police cover. There's just less police on the streets, at least at times I've observed. Cyclists do crazy things with impunity. However, Eastleigh centre is quieter than York's on an evening, with the exception of outside McDonalds where it's common to see kids clustering and strutting (in the way groups of kids can do when left to themselves). It seems to me that there are less drunken people. So maybe the Eastleigh police are being proportional too, though less apparently present and interested.
Funding has a big part to play in what policing takes place. National policy also steers policing. For example, Labour focused on a crackdown on street crime by getting more police on the streets and other similar initiatives. Some senior police were reported to find this move to be ignoring some greater threats, but street crime was visible and also a sure vote winner so that was the priority.
I imagine that when a community grows, and especially when a community has access to firearms, different techniques are required to effectively and safely police them. I can't imagine that being faced with the threat of being shot does anything to help a police force feel comfortable with the guy on the street.
That said, one retired senior UK police man I spent some time talking with commented that the nature of the police force had changed over the years and while he hugely enjoyed his time in the force (on "the job") he was less sure about the way the force had developed. I don't get the impression that marred his experience but that he disagreed with some of the policies and direction that UK policing was employing. I can't tell whether that was as a product of being old and obstinate or whether there was a more fundamental philosophical difference (and now can't ask).