This is widely popular as a rugby song, and likely also in the armed forces. It appears on broadsides from the mid-19th century. There are copies in the Bodleian library. The tune is the English show tune "Villikins and His Dinah", also known in America as "Betsy from Pike". The tune is also used for the Irish partisan song "The Old Orange Flute" and the Irish War of Independence song "The Bold Black and Tans". It is related to the jig tune "Paddy Whack". It is also related to the many variants of the "Derry Down" songs, which were very popular from the mid-17th century onwards. Originally political satires, they devolved into bawdy songs. It was collected in the early 20th century from tinker Annie O'Neil. It was printed in the Alan Lomax collection Songs of Seduction (2000), I can't recall where I learned this.