The tune is basically "Erin Go Bragh".

Oddly, I've heard "Johnny jump-up" given a quite different meaning - in Glasgow it used to mean people who would fill a glass with milk, jump up to a gas lamp, smash the mantle off, bubble the (coal) gas through the milk, and drink it to get high on the dissolved hydrocarbons and carbon monoxide. Some way downmarket of gluesniffing. Never heard of a song about it, though.