This over-heated debate about diversity in Roman Britain is skirting around one of the more interesting aspects of the nation's genetic heritage.
If Romans of African descent have left almost no trace in the British gene pool, Mary Beard is quite right to point out that neither have the Normans. (Or for that matter, any other kind of Romans.)
But more to the point, there is a notable (and for many, surprising) dearth of Anglo-Saxon ancestry in the English gene pool as well.
DNA studies tend to reveal that most 'native' Britons can trace their ancestors back in an unbroken line to the people that occupied the island long before the Romans even turned up, and that is this component of their DNA that tends to predominate.
This should not be all that surprising. After the ice age Britain was effectively an empty space that was suddenly repopulated both by people coming up the Atlantic coast from the Iberian peninsula and people crossing the North Sea from what is now Germany and Scandinavia. (My own paternal ancestors belonged to the former group, according to an analysis I had done a decade ago.)
Everyone who came later, Romans, Angles, Saxons, Jutes, Vikings, Normans etc etc. represented little more than a top-up.
Though from the political perspective the locals experienced this more as a top-down phenomenon!