Certainly some are Irish at least in part (The Bonny Bunch of Roses was set specifically to an Irish tune) but others don't appear to be, and were if anything more popular in England and Scotland.

One other song which clearly has developed from an Irish tune is Sam Larner of Norfolk's "Napoleons Dream" which, to my ear is certainly musically related to The Minstrel Boy.

Strangely I don't think it appears on The Frank Harte CD, possibly because it may only have been found in England, Irish tune notwithstanding.