In Saxons, Vikings, and Celts (2006), Bryan Sykes traces the genetic origins of Britain and Ireland through analysis of mitochondrial DNA (direct maternal lineage) and Y-chromosomes (direct paternal lineage). It's fascinating stuff if, like me, you geek out over the intersection between science and history. Sykes looks at what history and legend claim for British ancestry, then compares it with what the DNA tells us.
Basically, the British Isles are persistently Celtic. (Though Celtic doesn't necessarily mean what you think it does--think Celtic speakers who'd been in Britain since Mesolithic times or came by sea from Iberia rather than descendants of an invasion by the Celts of Central Europe.) Even in areas heavily settled by Saxons and Vikings, over half the mDNA and Y lineages are Celtic. And the maternal and paternal lines don't necessarily match, showing that invaders often fathered children with local women rather than bringing wives from their own people, and in some cases a "Genghis Khan effect," wherein one man or a closely related group of men is disproportionately represented in the gene pool.