Long before Brexit, and when I lived in the UK, I remember telling someone that I was going to Paris for the weekend, and she responded, “So you’re off to Europe then...”
And I’ve never forgotten, because it was such a strange thing to say
A lot of the "Normans as alien culture" atuff is heavily rooted in Victorian era (and beyond) views on British cultural origins and modern statehood, along with the idea of Britain as separate from Europe.
the archaeology and more recent scholarship increasingly shows that bleedover was constant.