UK voted to leave the European Union. UK remains in Europe Continent obviously.

UK is an island, not part of the continent.

Gibraltar...

... is not part of the UK itself. But it is under British sovereignty.

Which of the 7 geographical continents do you consider it to be part of then?

Obviously the English Channel separates the continental mainland and the UK. Geographically the UK is part of the British and Irish Isles. The UK is generally not considered as part of "continental Europe", but some definitions of Europe also include the UK geographically. It is debatable but I draw a line where the Atlantic Ocean clearly separates it from the mainland.

"North Atlantic" as a label for countries just a combination of Europe and North America north of the US-Mexico border. UK is "North Atlantic" (like most of the North Atlantic Treaty Organization) in that it is part of Europe.

EU =/= Europe

How is it possible to actually move the entire landmass? I didn't know we had the technology!

The definition of Europe is not a fixed historical constant. Including various islands in particular continents is an essentially arbitrary choice.

Europe as a geographic feature is a distinct concept from Europe as a sociopolitical entity. It is clear that Europe and the UK have been diverging culturally, socially, and politically for some time now.

UK does not have the political connections, open borders, collectivization of resources, harmonized regulations, shared currency, or really any other connection to the rest of the Europeans beyond memory.

politically yes - culturally or socially I don't see it a divergence. Very similar to rest of Europe