I must admit that when I lived in the UK I lived in both a city and a small town and both times I never knew my neighbors beyond saying hello if I saw them coming or going.
Here it is a different story though, we know nearly all of our neighbors on this street. They even give our daughter gifts on her birthday and such, and we help each other out with things that need to get done.
I think this effect is more cultural than it is anything else, I have noticed that people in this country are considerably friendlier than people in the UK. Everybody I pass either walking or riding a bike always says hi and you often see total strangers striking up conversation when waiting for the bus. I rarely saw anything like that in the UK.