I used to belong to a London club and used it as my hotel when I stayed in London. I just checked the rules. Sure enough, they still require a jacket for men.
"In all public rooms except the basement, Members and guests are required to wear jackets and long sleeved fully button-fronted collared shirts and follow a smart dress code. ....except June, July, and August."
I found FlyerTalk and was seduced by status/points/hotels. I gave up my membership a few years back.
(And I, too, love the Jeanne Moreau comment.)