There seem to be two black and white camps when talking about sub-roman but pre-germanic england: either the British were completely slaughtered and eradicated in all but Wales, or they were rather quickly assimilated into Anglo-Saxon culture.
The evidence of the former seems to be the historians themselves. Gildas speaks of "rivers of blood", though he seems to be what in modern times we'd call someone who "misspeaks a lot" (i.e compulsively lies). On the other hand, we have Y Gododdin, which seems to hold up to scrutiny quite well. That also claims that all the Northern Britons were defeated in a single battle, with four survivors (and conveniently, one of those surviving soldiers was the poem's author, Aneirin).
My point being... What's the evidence they weren't all eradicated, if historians who were there claim otherwise?
No, all evidence suggests that they weren't slaughtered. There was no near genocide of the Britons.
Most historians now completely discredit the idea of a massive invasion by Germanic tribes and slaughtering of Britons. It seems like there is new archeological evidence on this topic every single day. So, as it isn't my primary field I am sure someone will have more up to date information.
But it seems as though there had been steady migrations from the continent over a period of time. Archeological evidence has not given much to suggest a lot of battles took place. The old idea we had that the Britons were constantly being pushed back (but did some pushing themselves) that we see in later sources like Bede just doesn't match up. There surely was some raiding and it wasn't all some lovefest.
This is also inline with what was happening all over the Roman Empire before the collapse in the West (although that it was occurring does not mean it was the cause). As an example, the Franks didn't do a massive conquering of the people of Gaul. It wasn't all peaceful but mostly they stepped into the Roman void.
And that the migrations were probably relatively small. As was said above, DNA evidence does not suggest a drastic change in population. It suggests that the population has been relatively consistent since before the Roman conquest. All evidence leans toward the idea that the Saxons and co. blended with the surviving population but their language mostly controlled in "England" although not all of the British Isles.
What appears to have happened is that with the Roman abandonment of Britain their entire economy cratered. Rome leaving didn't just mean no army for protection. In fact, that may have been a relatively minor factor. It meant no Roman legions to supply. It meant all of the private business that moved in slowed or died out completely (iron extraction, tin extraction, large scale farming). Without the markets or massive trade cities like Eboracum or Londinium were likely reduced in population. So what you have is the British people, themselves, dispersing into the countryside.
It is also possible that there was a general exhaustion of the soil in existing areas. Which would have made many leave to find new plots.
Their own internal migrations match the Germanic migrations coming in. These people mixed up. There was fighting, as there always is (although, again, no evidence of any large battles). But it probably didn't line up perfectly along ethnic lines. Some Britons could have sided with the Germans. We have to remember that Britain was never a united kingdom. They had been conquered by Rome but most of them had little contact with Rome and maintained their own tribal allegiances. It doesn't follow that they would necessarily have more allegiance to another Briton tribe over a Saxon one.
Eventually the Germans began pushing to have larger territory and eventually kingdoms of their own. The stratification into distinct Anglo-Saxon kingdoms meant fighting other Germans as much as, or more than, native Britons. And that push likely happened long after they were already settled. It wasn't the purpose of the migration. Once they were settled some of their warriors may have been genetically Briton. Something to keep in mind is that the Germanic identity became important to the Anglo-Saxons later. As they were building new kingdoms the shared culture and language helped unite them. For the new kings having a long heritage of kingship in their family was important. Most of the Anglo-Saxon kings linked their family line straight back to their version of Odin (who is a little different from the Norse one but that's not important) or Thor, which means we know for a fact that they were beefing up the warrior/kingly credentials. It's possible that they didn't come in as invaders. But later the idea of coming in as invaders helped boost their own concept of who they were. It's an image they liked to have of themselves and their ancestors. And the legend became indistinguishable from fact. History is written by people who like to see themselves as the victors.
Robin Fleming's Britain After Rome is good for an interesting readable narrative. Guy Halsall's Worlds of Arthur is good for some of the legend making stuff I was referencing.
Like I said I'm a little behind the times. So, I'm sure there are better recent books.