My Dad used to sing the Alice song. I have never heard it sung by anyone else. Goodness knows where he learned it. The words differ slightly from the other versions but it is obviously the same song. Our family is from Hampshire, England.

Alice was very slender,
Alice was very thin,
She went into the bathroom,
Filled the bath up and jumped right in,
Her maid who was absent minded,
Pulled the plug out before she was through,
Pussyfoot Johnson save my soul,
There goes Alice down the hole,
Alice where art thou going?

When I was teaching I sometimes sang it to the children and I was always worried that a parent would complain that it had given their child nightmares.