Also a large genetic component of the Irish population is shared with people in the Iberian peninsula.

Yes, but the Iberian migration was just an earlier example of a long history of migrations and colonizations going back millennia. There was a time when the British Isles weren't populated by Homo Sapiens, and migrating people's found the lands empty (except for the occasional band of Neanderthals), but it's deep in pre-history and since then migration has almost always involved some level of population replacement and/or subjugation by new elites.