"This old man, he played one" continuing through ten verses until the old man "played ten" on some part of the singer`s anatomy or possession has certainly been sung by the folks, especially children, in Britain ever since Adam was a boy.
"He played nick nack on my drum"
"With a nick nack, paddy whack, give a dog a bone"
"This old man goes rolling home"
Also an interesting question. Why do we say someone is in a "paddy" when they are not in the best of tempers?