Basically, the further back you go in time, the more you have to assume that songs in English moved into, rather than out of Ireland . Lots of reasons: the strength of the Irish language , relatively limited literacy in English, location of printers etc. IanC is right that many of the songs effectively became a common pool with local variations.

There often seems to be a tendency to assume that songs are Irish in origin - because they survived longest in Ireland, in oral tradition. But of course, it doesn't follow! We should be thankful that the damn things DID survive - and not be too anxious to claim their origin. Such details are worth teasing out for the insights they give us into the songs and the societies from which they emerged but in the end - songs are for singing!

Regards