Britain wasn’t invaded in WW-II. Many of the EU member states were. A few of the EU member states were part of the Axis powers too and lost millions of people as well. The trauma of the war has led to the idea of a union of European states with more than just economic ties and trade they began with.
Britain never quite understood this idea despite also losing hundreds of thousands of people in the same war and being one of the countries that saved Europe.
They simply wanted the trading part of this EU project.
“Fog in Channel – Continent Cut Off”