We have them. Brits have them.
Run by the same people here as there.
Biggest difference is the size. Our shops are bigger and sell fairly common items at an astronomical price. When I go to the corner shop – here often known as Circle K or 7-Eleven – I go for a small bag of crisps (chips) or a fountain drink. Sometimes I’ll grab candy, too, but I rarely go there for anything beyond that unless I’m desperate.
On my first venture to England I had occasion to visit a corner shop and found it exactly as the Independent’s article describes… “it should provide the focus for a community by providing overpriced items that you may have forgotten to pick up from the out-of town superstore. Principal among these items are Pringles, Bourbon biscuits, cigarettes, pornographic magazines and bizarre cakes you never see anywhere but in corner shops.”