I realize that I'm not adding anything to the discussion, but just for completeness:

When I was a boy, I learned

Old King Cole
was a merry old soul
and a merry old soul was he
He called for his pipe
and he called for his bowl
and he called for his fiddlers three

And that was it - that was all I ever heard as a boy. But years later my wife supplied these additional lines

and every fiddler had a fiddle
and a very fine fiddle had he
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went the fiddler three

Don