Perhaps a good place to start might be the tramps and hawkers tune, this tune has been used over and over by songwriters for different lyrics, but gets altered slightly for different sets of words, take a look at the following songs that use this tune some with variation and some without, homes of donegal, rocks of bawn.
now try the dick darby the cobbler and its variants.
then we have lakes of pontchertrain , blarney rose.
Sweet thames flow softly,and trad tune used for recruited collier.
my opinion is that the tune gets altered slightly by the songwriter[ who is using a trad tune to fit the mood of the song and the lyrics