Formerly pretty widespead among children and Morris dancers, and known since the mid 18th century. See Iona and Peter Opie, Oxford Dictionary of Nursery Rhymes, no. 545, for detailed references (including the fact that the song, commonly sung to the tune of Lilibulero, was a favourite of Oliver Goldsmith's).

A Scottish form is in the DT: There was a Wee Wifie

In the Forum: Searching for Song: 'O`Sullivans March' (includes verse from Ireland formerly sung to that tune.)

I don't find any reference to Fife, though.