Hmmm... Checked wikipedia...

History of the Celtiberians

The earliest Celtic presence in Iberia was that of the southeastern Almería culture of the Bronze Age. In the tenth century BCE, a fresh wave of Celts migrated into the Iberian peninsula and penetrated as far as Cadiz, bringing aspects of La Tène culture with them and adopting much of the culture they found. This basal Indo-European culture was of seasonally transhumant cattle-raising pastoralists protected by a warrior elite, similar to those in other areas of Atlantic Europe, centered in the hill-forts, locally termed castros, that controlled small grazing territories.

...

According to the theory developed by Bosch Gimpera (Two Celtic Waves in Spain, 1943), the earliest Celtic presence in Iberia was that of the southeastern Almería Culture of the Bronze Age; in the 10th century BC, a fresh wave of Celts migrated into the Iberian peninsula and penetrated as far as Cadiz, bringing aspects of La Tène culture (5th century BC) with them and adopting much of the culture they found.

Goes to show how poorly this was taught in school back in my day... Now, the fact that there was a migration into the British Isles is not new

Sometime before 500 B.C., Celtic tribes began reaching Ireland, Scotland and Wales. Anthropologists believe that waves of different Celtic tribes migrated to Ireland and Britain over long periods of time. While many tribes came from the European mainland, a large number also migrated from the Iberian Peninsula.

but maybe what is new is the absence of a substantial migration from Brittany?

In any case, this

"Although Celtic countries have previously thought of themselves as being genetically different from the English, this is emphatically not the case," Professor Sykes said.

"This is significant, because the idea of a separate Celtic race is deeply ingrained in our political structure, and has historically been very divisive. Culturally, the view of a separate race holds water. But from a genetic point of view, Britain is emphatically not a divided nation."

seems to me tendentious. Humans are defined as much or more by their culture as by their genes. If an invading culture manages to convince the local people that they are not Celts, it's as good as if the Celtic population had been physically displaced. It's not as if Celtic culture is carried in the genes.

Those whom the Gods wish to destroy They first make mad. — Euripides