Wikipedia, of all things, gives the following additional information:

"'I'll Tell Me Ma' is a well known children's song. Originally written by Francie McPeake from Springview Street, West Belfast, Ireland. Johnny Murray lived across the street from the McPeakes and this is where "Old Johnny Murray says she'll die" lyric comes about. The chorus usually refers to Belfast city, although it is also adapted to other Irish cities, such as Dublin.[1]

"This song is Roud Folk Song Index number 2649."

The Clancy Bros. recording is titled, appropriately enough, The Boys Won't Leave the Girls Alone. It was their third album for Columbia and was reissued on a Shanachie CD now out of print. A used copy is listed at Amazon Music for $50. (Whew! Infla-a-a-a-a-ation!)

Bob