Last time I checked UK will still on the European continent for the foreseeable future ;)
It's always been just off the continent. I think they'd sail away if they hadn't been tethered to us by that tunnel.
Japan is also an island, but you don't see anyone trying to make the claim that it's not part of Asia. I wish people would stop conflating Europe and the EU.
From the UK, "the continent" refers very specifically to continental Europe, which means Europe without the British islands.
While Japan is an island, I would not consider it part of continental Asia, although that might be less of a common concept than continental Europe.