Old Rosin the Beau may have had an earlier life and it certainly passed into oral tradition, but it was published in the UK in 1844 as a theatre song in a play called ‘the Belle of the Hotel’. The sheet music shows it as written by actor and playwright, J B Buckstone, and composed by Edward Fitzwilliam Jr. The cover has a portrait of the singer, Mrs Fanny Fitzwilliam. She was an accomplished actress who was also well known for singing ‘in character’, anticipating the style of music hall singers of the following decades. I hesitate to claim this as the first appearance of the song in print, but it is certainly a pretty early showing. Some of the earliest music hall songs in the 1850s (for example ‘Villikens’) had had a previous life in the regular theatre.