From Wikipedia:

"Pretty Polly Perkins of Paddington Green" is the title of a famous English song, composed by the London music hall and broadside songwriter Harry Clifton (1832-1872), and first published in 1864. It was almost universally known in England until around the mid 1980s, and was commonly taught to school children. The title refers to the district of Paddington in London. The song gained a place in the canonical Oxford Book of Comic Verse, and the original manuscript of "Polly" is now held in the Bodleian Library.

It was adapted for the USA by Clifton during the American Civil War, re-titled "Polly Perkins of Abington Green". Presumably the new title referred to Abington Green, Georgia, in the USA.

Most of Clifton's songs adapted their tunes from old folk songs, and it is possible that a folk tune is also the origin of the tune for Polly. A folk song in the English county of Northumberland, called Cushie Butterfield, is sung to the same tune as "Polly" - although the "Cushie" tune was always claimed by one Geordie Ridley (1834-1864), a Tyneside comedian and miner. Ridley and Clifton's death dates mean that both the song and its tune are now firmly in the public domain.

The tune, with new lyrics, found its way into the Australian bush culture, among outback farmers and sheep shearers, in the song "One of the Has-beens".

[Note: the original text at Wikipedia contains several imbedded links that I haven't bothered to reproduce.]