Insist all you want, the English don’t regard themselves as European, they’re not on the continent and Princeton University agrees with this understanding. “Continental” is something of a derogatory term to the English. I know this well.
I was more using ‘continent’ in the geographical sense rather than the derogatory or cultural or opinion-oriented sense. Every citizen in Manhattan could detest North America and wish to be regarded as separate, but they would still be considered in geographical texts as being in North America, because they are on the North American Continental Shelf