According to military historian Donald Graves this song dates to the War of 1812. This is the best recording of it I know, but it's very hard to find. It's from Canadian Folksongs Centennial Collection, produced by the CBC, but never commercially available. Apparently the song was widely sung in Ontario in the 19th century, but wasn't actually published until the 1920s, if I remember correctly.

Note: Lieutenant Governor Simcoe was not a lord - my mistake.