I can't see any relation between the two songs. That above is Laws Q5, and undoubtably in DT. A late 17th century broadside copy is ZN143 in my internet broadside ballad index. It stems from a jest version, #62, in the earliest English jestbook, 'A C. mery tayls' (A Hundred Merry Tales), 1526. The song was also reprinted in 18th century songbooks.