'Suil Aroon'. The chorus might well be Irish but the standard text is pretty definitely Scottish. The tune, as you say, pretty universally used. Wouldn't like to even guess where that originated or how it evolved. There are plenty of instances of tunes being carried abroad in a variety of ways. Ach du Liebe Augustin is pretty universal. Huntsman's Chorus from Der Freischutz has long been a standard part of the English folk sessions repertoire. (Excuse spellings)