Regardless of what someone wrote in Wikipedia, The British Isles have not historically been regarded as part of the European “Continent,” to the point that English typically have not even referred to themselves as European. It’s because they’re not on the continent, they’re on an island. They may be in the EU now, but they’re not part of EU monetary union.
In most mainstream understandings of geography, Britain is considered to be European because it lies on the European Continental Shelf. Notice that Japan is typically considered an Asian country.