Biographies forget to mention it since there’s no evidence of him belonging to any such club. Also those clubs reputation is probably highly exaggerated. Your main source is some London tourist guide -site, so doesn’t seem you did exactly stellar research here.

If you are interested in rich elites of the time doing strange and sordid festivitoes, I recommend studying the life of Peter the Great of Russia, who really was not very great at all as a person, but his drinking parties were literally insane and deadly. Empire and Rest is Hostory has great podcasts on him and there’s several good biographies available in English.