Chris, Mundesley was for TB (see above).
Thanks, Adam. I learned about Warneford, fwiw, in Ved Mehta's Up at Oxford (1992).
Greg, while Mundesley was originally for TB, it became a drug and alcohol rehab center in the 1990's. Last year, however, it opened as a mental health treatment center. It was 18 holes but was reduced to 9 holes at some point and I'm not sure whether those currently remain.
I mentioned Vardon's ace because while he was at Mundesley for TB, it's likely the rest and time from golf helped with his exhaustion, stress and possible bouts with depression alluded to in, "The Greatest Game...." Borrowing a golf club and after having not played for a good time, he goes out at the suggestion of medical personnel and scores his one and only ace, ever.
At any rate, I believe Mundesley falls into what you were asking in large part, although I don't know about the clubhouse.