So to return this into its geographical context, is some random blogger on the official government cartography experts Ordnance Survey right or wrong?
FTFY.
We don’t know who wrote that article, it could have been the cleaner for all we know. Aside from that one blog page can you find that definition anywhere else? I can’t.
On the other hand, googling “britain definition” gives us:
https://www.collinsdictionary.com/dictionary/english/britain
another name for Great Britain, United Kingdom
https://www.dictionary.com/browse/britain
Great Britain.
Britannia(def 1). [which says it’s the Roman name for the island of GB]
https://www.thefreedictionary.com/Britain
Several definitions that repeat the above, and a hilariously unfortunate thesaurus entry. Go look. (-:
https://dictionary.cambridge.org/dictionary/english/britain
England, Scotland, and Wales
And many more all saying the same thing. Quite where the OS blogger got their ‘technically just England and Wales’ claim from I don’t know and they don’t cite any source for that. If there’s some sort of legacy explanation from centuries ago then I can’t find it.
So I’d say yes, by dint of weight of evidence to the contrary, they’re wrong and it’s false authority syndrome.