I know this is an old thread, but since there's been continuing interest in it, I thought I'd add one piece of information which a search indicates hasn't been included before.

The rhyme occurs at a significant place in Alfred Hitchcock's film Marnie, where a group of girls skipping rope chants it in the following form:


"Mother, Mother, I am ill.
Send for the doctor over the hill.
Call for the doctor.
Call for the nurse.
Call for the lady
with the alligator purse.
Mumps said the doctor.
Measles said the nurse.
Nothing said the lady
with the alligator purse."

The lady, I think, is death.

Someone who's also seen the film has told me that she knew this rhyme in a closely similar form when growing in the 1950s in the American Midwest.

Jon Corelis
Songs by William Blake