Bodleian, Harding B 11(2916) - The Cow Eat the Piper

I first came across this in the every invaluable The Faber Book of Popular Verse (1971), and first heard it sung by Geoff Burton who was a student in Durham in the early 1990s. The melody he used has echoes of The Limerick Rake, and though I never did ask him where he got it from this is the melody I use today. The story of The Cow that Ate the Piper is a common one in the storytelling community (where there is a greater sense of comeuppance by way of a conclusion) though I've never come across a collected source.

So what came first I wonder? The story or the ballad?