If you want a philosophical (if somewhat meaningless) argument, Vic I suppose the answer must be that by virtue of my birth to English parents (themselves English as far back as I can trace), all of us living in England for all of our lives, probably qualifies me as English as far as I am concerned. My recognition (or otherwise) of the Monarch is immaterial to my perceived nationality.
A person's nationality is generally accepted (with few exceptions) as what they perceive it to be, and I am quite happy with mine.
It is true that the UK is part of Europe (as it is part of the world). That is a geographical matter, not a political one.
Changing one's nationality is usually a bilateral arrangement and , as I said, nobody consulted me.
Will that do?