I have been living in the UK for almost 10 years. It's funny because at work some of my friends talk openly about the immigration issues the UK is facing. When I said I was an immigrant, one said, no your not, you just returned from the colonies. Even though my accent stubbornly stays American I have been accepted by the majority of the people I have met.
I have lived in the South East, Midlands and Scotland. In the U.K. there is a vast difference between people from the South, North, North East, North West, Midlands, Yorkshire etc. The accents are different, personal views, culture etc change from area to area. In some places the idea of driving farther than a few roundabouts is not worth the trouble. In others, commuting from Nottingham to London is common. If your an American wondering what it's like to live in the UK I suggest you read Bill Bryson's Notes from a Small Island. My wife bought it for me when i first came over and it proved a great read and invaluable.
I have only had trouble with 2 people since I moved here. And thats a heck of a lot less than in America. There is a troubled gentleman I see on the bus. He is convinced I am best friends with George Bush, work for the CIA and could get him a job in the states. Occasionally he gets a bit aggressive about needing a job in the states. Luckily, I moved so I see him less and less. The other person was harassing me in a pub, when I was trying to get drunk btw, for being an American. It's hard to argue about where your from, I suppose I should have told him I was Canadian.