Ed Cray, The Erotic Muse, p. 131, says "This song seemingly began life in English music halls, probably during the latter half of the nineteenth century, and must have acquired bawdy verses early in life."
A text given by Cray (A) was given to Robert W. Gordon in 1923, No. 246 in the Gordon Collection at the University of Oregon and the Library of Congress. This is the earliest collection known to Cray when his book was first published in 1969.