I just finished reading Stephen Oppenheimer's Origins of the British. As a biochemist, I'm excited to see tools that biologists have developed used to contribute new theories to the historical field.
However, I find two of his historical claims to be exceptionally different from what I've learned from conventional history all my life, and I didn't find his evidence as convincing as his genetic evidence:
Is there serious scholarly support for the idea that Celtic languages arrived in Britain much earlier than the spread of Hallstatt and La Tene cultures? If so, what does that mean about these cultures if they were not a linguistic spread?
Has any new research come out since the book was published that corroborates his claim that the Belgae of Caesar's time were actually 'Saxons' in Britain? Do we know anything else about their identity, be it Germanic or Celtic?
With regards to the second claim, few historians of the Saxon period would take it seriously. While our sources for the coming of the Saxons are poor/non-existent, it is apparent that there was Celtic settlement in the area of the Belgae and there seems to be the idea from both fellows like Bede and Gildas that the Saxons were a foreign invading force, even if the start date for such a claim is not reliable. It is likely/almost certain that the number of Anglo-Saxons in Britain during the invasion/migration were lower than those of the native Britons, but those native Britons especially in eastern Britain appear to have assimilated fairly quickly.