I live in an apparently 'Little Britain' type city in Canada (Victoria, BC) although it's usually only called that by people who have not been here, have not been to Britain or by people who market the city as a tourist destination.
Yes, there are some nice Victorian homes but step away from them and the contrived 'British tea rooms' (none of which are owned by British people) and it's just a very west coast Canadian city: lots of greenery, lots of mountains, lots of water, lots of people from somewhere else, lots of Native Art, lots of homeless people and lots of guppies, yuppies and hippies.
To underscore my point, ages ago Neil posted a photo of red phone box on his blog. I thought it would be a snap to find one or two locally since it's apparently so British here. I have tried to find some British phone boxes in 'British' Victoria. I even asked at the tourist office. Nope, they didn't know where one might be... eventhough photos of them are on tourist brochures. (excuse me while I roll my eyes).
I stopped thinking about it until I was just flipping through some of my photos from the wild west city of Cowtown, Alberta and wouldn't you know it.