Oxford’s Bryan Sykes, who invented the genetic population testing method, has written some interesting books on this subject, too. In “Blood of the Isles,” he wrote that neither Anglo-Saxons nor other population groups have much impact on the genetics of the inhabitants of the UK, except for Iberians, and that British ancestry can be traced back mainly to Spain. Fascinating information. I heartily recommend his “The Seven Daughters of Eve.”
I recommend Syke's newest book too: Saxons, Vikings, and Celts: The Genetic Roots of Britain and Ireland . A very good book and easy to read. Oppenheimer's is the better of the two though.
So the Celts and the Ango-Saxons are like the Normans: Invasion forces large enough to take over those who already inhabited the land. Maybe the Brits are set-ups for the Muslim invasion.