In his book "One Voice: My life in Song" Christy writes that he first came across the song when "I was staying in a house in Derry after an H-block concert and a young lad recently released sang this song..."
from here


Summary, as I see it:

GF wrote the W of the EF to a remembered melody which he says was an old Irish folk song.
Bobby Sands wrote BH in D to (basically) the same tune- probably after hearing GL's melody. CM heard it sung complete and popularised it.