According to Roy Palmer in 'What a Lovely War' p35. the tune is 'Solomon Levi'. I only have one copy of 'Solomon Levi' with tune and that's in Pankake's 'A Prairie Home Companion Folk Song Book'. Looking at the tune there it is a little like that used for 'Rumpsy Bumpsy Ay' and 'Eleven More Months and Ten More days I'll be out of the calaboosh'
Jig time, fist 2 bars all on one note, next 2 bars one note a tone up, and the next 2 bars a tone up again.