> Is this game well-known enough in Britain and Ireland that readers will know what on earth is being alleged just from reading this article?

Absolutely. Very well known.

My Youtube-fu is not with me, so I can't seem to locate this video on Youtube, but see this BBC Archive footage from 1971 that was posted on Instagram[1] from a BBC News Report entitled "Conkers is no longer a kids' game."

[1] https://www.instagram.com/bbc_archive/reel/DA7zkmkAShz/