hi! it might be worth getting the input of /r/AskScience: there are a few theories that have come out of genetic research. Meanwhile, these previous discussions may be helpful

• How did English, as we all know is a Germanic language, become the prominent language in Britain when, as I've read that many historians believe, the number of Anglo-Saxon migrants was small relative to the number of Native Britons and Romano-Britons?

• What happened to the native people of Britain, particularly England

• Did the Anglo-Saxon conquest of Britain involve mass migration that pushed the Celtic people to the North and West?

• What are the current views on whether there was a post-Roman mass-migration of Anglo-Saxons to Britain during the dark ages or whether it was mainly a cultural and technological change with the ruling classes most affected by warrior migration?

edit: found a bunch more which may help flesh out the story from various perspectives & provide additional sources

• Were the migrations of Angles and Saxons to the British Isles peaceful or violent?

• How much effort was put into maintaining Roman construction after the fall of the Empire?

• Would most people in England (as defined by it's modern borders for the sake of simplicity) consider themselves Roman, Briton or Saxon in AD470?

• thread in Wednesday AMA: British Military History

• thread in How did the decline and fall of Ancient Rome affect the average citizens of the Empire?

• Why were the Brythonic people unable to protect themselves?

• Did the Romans simply leave Briton with the collapse of their empire

• What is the difference between Celtic, Gaelic, Brythonic, and Welsh? When did they become distinct?

• What remains of the Britons, aside from place names?

• Britons during the Anglo-Saxon period?

• How many Britons(Brythons) survived the Anglo-Saxon and Norman invasions and lived to reproduce?