Interesting article. Genetically, it's not that surprising that the populations go back before the Celtic and subsequent invasions.
But you can't discount the importance of cultural change. China had a way of assimilating invaders and getting them to adapt the Chinese culture. But the Celts, the Anglo-Saxons, and the Normans all ruled in their turns, and had enormous cultural influence. Which would help explain why the people of those regions are so different from one another.
At the time of the Germanic Invasion of Britannia, the inhabitants were called Britons, as in Arthur, King of the Britons, for you Monty Python fans. These people were pushed to the west -- to Wales. Many others settled in France -- Brittany. The Angles/Saxons/Jutes did not kill everyone, they just forced their capitulation. Eire was spared this invasion. Subsequently, England was invaded by Danish Norsemen, and Eire by Norwegian Norsemen, (the Fitzes). Each wave of invaders imposed their language and culture on the conquered peoples. The Irish, Scots, and Welsh all speak a form of the language of the Celts -- Gaelic or Gallic, as in Gaul.