I'm surprised that anyone feels confident enough to say what happened to the Britons for sure. AFAIK its not even proved very clearly one way or the other whether the Britons left England (either by forcible migration or being killed) or whether they stayed more or less where they were, and the Anglo Saxons lived along side them and intermarried, and it was only Saxon culture that became dominant.

Rather in the way that when the Romans came the population stayed more or less the same but the Roman culture was widely adopted.

In fact the last I read was more in favour of the intermarriage/culture option.