Alfred Tennyson opined that simple faith (was more) than Norman blood, and Tennyson may well be right.
Stephen Oppenheimer, one of the most prominent British autorities on DNA research, is contending that there simply isn’t all that much Norman blood around in Britain anyway, nor Celtic, nor Roman, nor Anglo-Saxon.
According to Oppenheimer,
Everything you know about British and Irish ancestry is wrong. Our ancestors were Basques, not Celts. The Celts were not wiped out by the Anglo-Saxons, in fact neither had much impact on the genetic stock of these islands…
The genetic evidence shows that three quarters of our ancestors came to this corner of Europe as hunter-gatherers, between 15,000 and 7,500 years ago, after the melting of the ice caps but before the land broke away from the mainland and divided into islands. Our subsequent separation from Europe has preserved a genetic time capsule of southwestern Europe during the ice age, which we share most closely with the former ice-age refuge in the Basque country. The first settlers were unlikely to have spoken a Celtic language but possibly a tongue related to the unique Basque language.
Another wave of immigration arrived during the Neolithic period, when farming developed about 6,500 years ago. But the English still derive most of their current gene pool from the same early Basque source as the Irish, Welsh and Scots. These figures are at odds with the modern perceptions of Celtic and Anglo-Saxon ethnicity based on more recent invasions. There were many later invasions, as well as less violent immigrations, and each left a genetic signal, but no individual event contributed much more than 5 per cent to our modern genetic mix…
based on the overall genetic perspective of the British, it seems that Celts, Belgians, Angles, Jutes, Saxons, Vikings and Normans were all immigrant minorities compared with the Basque pioneers, who first ventured into the empty, chilly lands so recently vacated by the great ice sheets.
By “Basque pioneers,” Oppenheimer is referring to female-line mitochondrial DNA haplogroup H1.
mtDNA Haplogroups in general.
Oppenheimer has a new book on all of this, titled The Origins of the British: A Genetic Detective Story.