Good work, Gargoyle, and something I ought to have thought of trying. It often does work when there are 'orphan' webpages lurking about.

Judging by the verses, the 1915 song was probably written to capitalise on an existing parody doing the rounds among the troops. Whether there was ever any more to that than the words we still know might be hard to establish, but it may be that the answer is out there in memoires of the period and the like.