The original poster is not altogether correct. Rose of Allendale is about Katherine O'Shea, Parnell's wife - Allendale is his house in Wicklow. Danny Boy is Irish. Mountains of Mourne was written by Percy French, who was Irish last time I looked.

Song for Ireland is a song about Ireland by someone called Phil Colclough - I've heard the song on the radio but don't know anything about it. Someone will know, I'm sure.

Peggy Gordon is certainly sung in Ireland as a traditional song; I don't know its provenance.

The Shoals of Herring is, of course, English, by Ewan McColl, and a great song it is too.

Fiddler's Green - don't know where it comes from but the phrasing certainly sounds English.