Quite often - particularly in the media - I see British examples of things being referred to "A Very British... " whatever it is
e.g. a documentary about the British building their first nuclear bomb was called "A Very British Bomb" - but, OK it was British in that it was made in Britain, but I couldn't see what was "very" about it... (It didn't spray tea and crumpets everywhere or anything)
I don't see it applied to other nationalities (e.g. you wouldn't really see "A Very French... " or "A Very Irish... ")
A quick google search for "A Very British" shows up loads of examples, but noticeably a book from 1982 called "A Very British Coup" - are they all spawning from that or is it just another example?
To clarify, I'm not just talking about the words "very British" but more the commonality of the use of "A Very British" (I'm not sure of how I'd explain - perhaps that needs another question!) almost as a title or a self-contained grouping of words.
For example: If I asked you where does the common usage of the words "Big Brother" come from, you might say George Orwell's 1984 (if not the TV show! But even there it originates with 1984) - it has a specific use outside just a brother who's big. You probably wouldn't tell me there's nothing special about "big brother" just because a google ngram shows that "little brother" is used more than "big brother"