I am indebted to the artist Robert Tilleard for pointing out that it is Brooks's Club of St. James's, not Brooks' Club of St. James'.
Checking with Fowler's Modern English Usage (1926 Edition) I find that leaving the extra 's' off was the early form, but it is only these days (or at least in 1926) done in Poetry and in reverential style. I distinctly remember being taught to leave it off, but then my old Headmaster, Walsham Temple Crewe Maynard, dated from pre-1926.
Incidentally, the spell-checker on the blog allows Brooks' but not Brooks's. But Fowler rules.
I like a bit of pedantry and have accordingly changed the blog title.