A search of the Bodleian Ballad library turns up a lot of songs from as early as 1855 which were already using the tune.

Examples

Nicholas and his rhino ("'Tis of a rich tyrant who in Russia did dwell ...")

The great prize fight between Morrissey and Heenan, the Benicia boy, at Long Point, Canada, Oct. 20, 1858 ("Ye merry gay sportsmen, wherever you be ...")

The back-door commission; or, The fiat against publicans and publichouses ("Shut the back-doors, lads, but first let us in ...")

Nedward and his Fanny ("It's of a young clothier I'm going for to tell ...")

Albert, Victoria, and Napier ("As Victoria and Albert together did stray ...")

John Dean and his own Mary Ann. Or, the gallant young coachman and the cruel father ("Oh listen to me while a story I tell ...")

Teetotal Sam ("Two jolly old fellows, some four months ago ...")

The Sunday trading riot ("Oh, my friends have you heard of this terrible job ...")

Susy and Pat Murphy ("Och, it's of a rich farmer in Limerick did dwell ...")