I'm pretty sure the full history as known must be in the DT somewhere.
It appears that the original was 'Jack the Chimney Sweep' as printed by Pitts in London. Jack was a real life chimney sweep who stole chimney pots and sold candles short of weight. In prison he was advised to give up drinking but whilst going up Holborn Hill to be hanged he was allowed to stop the cart at St Giles' for a last tipple before being hung at Tyburn. He was hanged in 1701 so Pitts printing was over a century later. His 'last goodnight' song put out by the likes of Pitts became very popular on the streets and then was taken up by W G Ross as 'Sam Hall' and sung with great venom and drama by him at the Supper Rooms like The Coal Hole. It then became even more popular in this form with the middle class merchants and was even more widely printed. Its popularity on the streets lasted well into the latter half of the nineteenth century which is presumably when the bawdy parody 'Nobby Hall' was penned. It's very difficult to date these bawdy parodies as they weren't written down till the middle of the 20th century. Ed Cray gives a long history of this and related songs in his book 'The Erotic Muse'. He misinterprets a comment from Joseph Ebsworth on the blasphemies in the song as the bawdy version, but Ebsworth is more likely referring to the swearing in Ross's version. I'd say it's more likely that the bawdy version arose more towards the end of the 19th century long after Ross was dead.