While this is the traditional view, my understanding is that DNA testing has shown that, in fact, the Saxons implanted themselves as a ruling class over top of the British agricultural class, pretty much in the same way as the Romans did before them and the Normans did afterwards. Most modern people of English stock are, in fact, British.

On a side note, while I've not played them, a few years back a rule set named "A Glutter of Ravens" was published specifically for this period.