But as for the anglo Saxons? I think they came over in waves and integrated with the native population. I'm not saying that they were all displaced (though Wales would probably have been a refuge) but my guess is that unlike earlier shifts, this one was initiated by invasion and integration.
I am glad you said that, I couldn't agree with you more. Migration and eventual integration, after a great deal of fighting spread over a long period of time. Displacing an entire peoples just wouldn't happen, although many settled in mainland Europe as well, the Britons had been bullied into submission before by the Romans so they weren't going to let the Anglo-Saxons invade and take over without a good fight. Because this period went on for so long it was inevitable that integration was going to happen eventually and the result is a huge mixing pot of different peoples (inc. the Jutes and I am sure there are a couple of others but can't think off the top of my head which ones) forming what is essentially a new people, whether they liked it or not. I know this is a major oversimplification but I find it fascinating that we (as in peoples) all came from somewhere else :D