Speaking of Joe Cocker, this is from the classic "Mad Dogs and Englishmen" album, which was recorded live at the Filmore East in NYC back in 1970. Remember Delaney and Bonnie? The tour of, I think, the same name, was put together using members Cocker had associated with from the Delaney and Bonnie and Friends gigs from around the same period, including Bonnie herself.
Tulsa boy Leon Russell on piano.
Speaking of Leon Russell, other than his "Ballad of Mad Dogs and Englishmen," the studio version of which is included on the later release of the Joe Cocker album, as far as I can tell, that is the only reference to what appears to be Noel Coward's song from 1930-something, "Mad Dogs and Englishmen." I haven't found any other references to the phrase "Mad Dogs and Englishmen."
I remember hearing the Noel Coward song as a kid, though it seems to be a novelty song among a certain college "in" crowd. By "in" crowd, I mean generally older folks like my father, many times veterans who had been in WWII, and who were taking advantage of their GI Bills to go to college. They weren't exactly with-it the way the students just out of high school were, but there were enough of them that they had their own culture; much of it borrowed from folk, jazz, the beatniks, and so on.