If it's a kit based on an American interpretation of the style - like Redhook ESB, for example - then American ingredients are totally appropriate.
There are also American ingredients that make good English ales. Willamette hops, for example, are an excellent substitute for Fuggles, with many of the same characteristics. White Labs Cal V yeast (WLP051) is nice and fruity as well as a medium attenuator, which makes it a good candidate for English ales.
Further, some British ingredients won't have the characteristics you find important. Muntons, for example, is the only widely-available British malt extract. But any experienced brewer can tell you that Muntons extracts tend to ferment very dry. That makes them inappropriate for a fuller-bodied English ale.
Thus, you could brew a supposedly English ale with all English ingredients and end up with something pretty crappy, compared to commercially-available English beers. Conversely, you could brew an English ale with American Willamette hops and Cal V yeast, Belgian specialty malts, and German pale extract and end up with something fantastic!
While it's nice if a kit for "English Brown Ale" contains only British ingredients, it's not strictly necessary. You dig?