With Irish singing, all singing sessions are Irish only. Because as soon as they sing it, it becomes Irish. From Courting in the Kitchen via Off to Dublin in the Green to Dirty Old Town (and Shores of Erin).

As others have pointed out, many tunes in the Irish repertoire seem to be Scots or English in origin. And French these days. I didn't manage to get Baym Reb'n in Kilfenora accepted though.