The tune for this is "Galway Bay". "They're moving Father's grave to build a sewer" is a classic music hall song. The origin seems to be unknown but was revived by the Clancy Brothers. It was a favorite of Frank Muir's, well before the Brothers' time, who sang it many times on BBC Radio 4. Except for the bathroom humor, it's not nearly a truly bawdy song. I can't find any background yet. I learned this from The Clancy Brothers.