Once you start thinking with a British Accent (like speaking a foreign language - you become fluent as you're able to think in that language) American accents (or similar) tend to stick out sorely when you're out and about, especially if you live in an area where you don't hear them that often.
Whenver I go to London (which isn't often) I can always find Americans, but I think it's more because of the work / tourist draw more than anything else. Most companies have their headquarters or main base in London, opposed to other cities around the country...
I know our village is small, but I can't lay claim to being the only American in the village. It's funny when you're on forums or in meetup groups and people are adamant they're the only person in x city (even though there are people on same forum / group living in the same place).
In our village I know there're a few Canadians (one woman I used to speak to regular, repatriated back to the UK as a child - her parents were originally from the village, but she spoke in a mixture of Canadian / Yorkshire - she said she still has a hard time living here and she was well into her 40s). I've heard there were other Americans in our village, but yet to meet anyone. One of the Mums I met from our local Sure Start Centre says her husband is a British and American dual citizen despite originating from Sierra Leone. Ironically as well there's another American woman that work's at the village High School and she's American and lives nearby and another American woman that lives a couple villages over as well.
When I'm out and about in Sheffield I don't really hear a lot of American accents, but then again Sheffield's not exactly a tourist hotspot...