[JohCol]

The Irish are, like the Scots, and the Welsh, and the Bretons, strongly genetically matched with the Basques. But then, so are people of all the regions first populated by the 'proto-basques' who descended from the Pyrenees aftger the last Ice Age: Northern Spanish, and Portuguese; Western and north western French, and, Icelanders, seeing as how they are largely a blend of Western Norewgians (likely more Basque themselves than the rest of Scandinavia) and British Islanders.
As for the original divide, it seems likely that groups that over-wintered in the Balkans, and later moved into Germany also moved in to England, and so were related to who were to become Anglo-Saxons, long before we knew who the Angles et al were; meaning that the proto-basques likely lived next to small groups of non-proto-basques, the latter were 'stranded' on the Island, and were subsequently 'celticised' during the first invasions from teh Contintent, and then, subsequently, 'Teutonicized' BY THEIR OWN GENETIC KIN once again -- the Anglo-Saxons. That is why so many Britons were so easily absorbed in to the Anglo-Saxon society and why you can very seldom tell them apart...not because anglo-saxons conqured Britons, but because the Britons, to a considerable degree, were ALREADY very much like the Anglo-Saxons, and their continentalist kin, the Celts.

[Cronos]

That is why so many Britons were so easily absorbed in to the Anglo-Saxon society

Are you sure? Most history shows that the Britons were pushed back by the invading GErmanics and moved into Cymru (Wales) and Cornwall. Their land was occupied by the Angles or Saxons or Friesians