It must have been quite old, because a song in the Bodleian collection dated between 1683 and 1696 gives the tune as Blue Bells of Ireland. The chorus to that one is

And the Blew Bells of Ireland rings well and rings well
And the Blew Bells of Ireland rings ding dong Bell



Joyful news for Maids and Young women
(about a shipload of white puddings)

I believe White Puddings and Beetroots both refer to the same part of the anatomy!