I'm due to do a full study on this song in the next few weeks for the forthcoming new book in the Marrow Bones series. The fact that there are at least 3 different printed versions in the early 19thc tells us that the song dates back to at least the late 18thc. The style and language are that of the London Pleasure Gardens like Vauxhall and Renelagh. The earliest dated version I have is by Robertson of Glasgow, 1802, but I have references from the 18thc in songsters. Even these vary.