Sorry about throwing in 'The Sporting Hero' red herring. It's actually just another broadside title for WITJ. What could be relevant though is that the WITJ could be the music hall title based on the earlier broadside title TSH hence designating the tune from the broadside version.
IMHO the words of the chorus on the GBB broadside fit well enough to the current tune if you slow it down to Denny Bartley speed. I would suggest that like many old songs the tempo has been much jazzed up for modern-day ears a-la Thin Lizzie.