I know it via Allan Block who sang a modal version (Mixolydian; chords were G and F) which went

Polly put the kettle on the little one the big one
Polly put the kettle on we'll all take tea
Slice of buread and buttermilk is good enough for anyone
Choose the one you love the best and bring her home to me
Oh dear _____ (girl's name) how I love you
Nobody else do I love like I love you
Heart you have, hand I give you
One more kiss before I leave you

which is AT LEAST as much fun as Gid Tanner and not as well known./ Wonder where Allan got it. . . maybe I can ask him at NEFFA! PETE