I recently finished Saxons, Vikings, and Celts: the Genetic Roots of Britain and Ireland by Bryan Sykes. It would have been a lot more interesting (and it was pretty interesting, mind you) if Sykes had devoted more pages to interpretation and implications than to the quest for DNA samples and thumbnail histories of the Isles. (BLOGGER ETHICS NOTE: I had to buy the book with my own money and did not get a damned thing for reviewing it. Nobody asked me to review it, and it is unlikely that anyone will be inspired by this review either to acquire the book or to eschew it.)
Anyway, the analysis shows that the long postulated Celtic invasion from Central Europe does not show up in the genes of the Islanders. On the matrilineal side, the Islanders are mainly descended from the mesolithic foragers who first resettled the Isles following the last glacial retreat up to 10,000 years ago. There appears to have some movement along the Atlantic coast from Iberia in the early Neolithic. In Orkney and Shetland, it appears that the Vikings brought their women with them when they settled the area (about a third of the folks carry Viking mDNA). In the old Danelaw, there is evidence that women came with the Danes or the Saxons (5-10% have Viking, Dane, Saxon or Norman mDNA). There is almost no sign of Roman genetic influence in mDNA.
On the patrilineal side, the vast majority of male Islanders carry a Celtiberian Y chromosome. There also seems to be a substantial minority who carry the Y of the mesolithic aborigines, and there is an overlay in the East of Saxons, Danes, or Vikings (in East Anglia as much as 20%).
All in all, the Islanders are Celts (their ancestors antedated the Romans and spoke Celtic languages). Englishmen, Irishmen, Scotsmen, and Welshmen are all brothers. Suck on that, WASPs!