i thought genetic evidence had shown that it was migration + assimilation of the natives? the modern english show a mix of saxon and brythonic ancestry.

Yeah no doubt some areas had assimilation, intermarriage. And of course then some intermarried clans migrated internally too, both in the 5th-6th C looking for land and later fleeing Norse invaders. But some areas also show resistance and/or mass flight too. Part of why the answer is convoluted.