Cecil says in his column, “Amazingly, the Anacreontic Society still exists in England.” No, it doesn’t. What exists is a modern Scottish re-creation, which is a very different kettle of fish. The original Society has been moribund for centuries; the wording of Cecil’s column gives a very different impression.
The Anacreotic Society does to exist! They have a web page.
You can hear them sing To Anacreon in Heaven too. After listening to it a couple of times, I now know why their reputation as a drinking organization over shadowed their reputation as an organization that promotes music.
They exist now and they existed then. What the OP is saying is that the current one is not the same as the old one, but rather a modern revival of it.
And TAIH is a terrible song - you have to be drunk both to sing it and to listen to it.
Actually, that makes it a marvelous song.