I think there’s a relatively simple explanation here. Ireland is just a hop across the sea, first gen Irish people come over because they have a decent job already lined up here or qualifications that mean their employment prospects are good here. Irish people who do not have good employment prospects probably aren’t going to move over to work in a supermarket? And those who don’t find that their employment prospects are any better here more than likely end up moving home.
That’s assuming it’s just first gen we’re talking about. Otherwise I get to gloat too because both me and my wife have Irish in us

(both of my wife’s maternal grandparents are full blooded Irish which I guess makes her mum full Irish too although she was born in Engerland. I’m 4th gen on my dad’s side - but that still counts right?)