Well, I should have read the thread more carefully. It is indeed in Broadwood/Fuller Maitland of 1893, as per the Ballad Index reference above.

But Lucy B took it from Marianne Mason's book of Nursery Rhymes and Country Songs (1878).

Ms Mason's note says: The tune is sung in Lancashire. There are no words, properly speaking, beyond the first verse, but rhymes are invented according to the pleasure of the singer. The melody is that of an old Christmas Carol, "There were three ships came sailing by".

Despite its absence from my copy of 'Songs of All Time', this book does cite Broadwood/Fuller Maitland as a source, so that must be a link to Jean Ritchie, either from a different edition or from one of the other songbooks in the series. (I'm sure I have seen the song in one of these, but can't find it at the moment - I'm afraid my library is a bit of a mess).