I’m interested in the fate of the Romano-Britons and the vestiges of Roman culture on the island of Great Britain in the period following the departure of Roman authorities and during the formative years of Anglo-Saxon settlement. My rough understanding drawn from media such as The Last Kingdom and other fictional depictions of the period was that the future Welsh/Cornish peoples held onto a sense of their Roman-influenced heritage long into the period of Germanic occupation. Indeed, the consensus appears to be that most famous Welsh folk legend, that of King Arthur, seems to be widely held to be a corruption of legends surrounding the lives of post-Roman Britonnic leaders fighting the investing Anglo-Saxons. However, the map heading the Wikipedia article on Romano-British culture seems to indicate that the future Wales and Cornwall were among the least romanized regions of Roman Britain. Later in the same article is another map showing that the Britons has already lost control of the most romanized areas of the island by the 6th century and we’re beginning to be restricted to Wales, Devon, Cornwall, the Lake District, and Galloway. This leads me to a few questions. If the areas where Brittonic language and culture survived after Anglo-Saxon settlement were the least romanized areas of former Roman Britain, then to what extent was there any influence of Roman culture on the medieval Britons? And, what happened to the Britons in those more Romanized areas which were settled by Anglo-Saxons? Did they move west and north to join their brethren, or were they subsumed by the Germanic newcomers? And, given that Christianity (brought to the island by the Romans) survived amongst the medieval Britons but did not make substantial inroads into the Anglo-Saxons until the Gregorian Mission, did Christianity itself carry cultural connotations of “Roman-ness” to the Britons who practiced it in the early medieval period? I’m generally interested in anything and everything related to this topic, so if you have something to add about it even if I didn’t explicitly ask, please enlighten me anyways!
I answered a somewhat similar question here, focusing on literary culture and historical memory. There's undoubtedly more to be said from perspectives like archaeology and church history, which I'm less familiar with.
To touch briefly on some of your questions here which aren't addressed in that answer: there are a number of different approaches to thinking about what happened to "Britons" in areas settled and ruled by "Anglo-Saxons," but many recent studies have emphasized the fluidity and social contingency of these identities, in contrast to older, more ethnically essentialist scholarship. The majority of Britons in the lands that became England probably assimilated over the course of generations. This may be the process we see at work in the royal family of Wessex, whose founder, Cerdic, bears a Brittonic name. Even as late as 689, the King of Wessex had the clearly Welsh-derived name Cædwalla. In the law-code of Cædwalla's successor Ine, a distinct and generally inferior status is ascribed to his subjects who are wealas, "Welsh," implying that at least some people bore this identity into the early 8th century--but also that there may have been incentives to identifying as English/Saxon. However, some British subjects of Saxon kings did not assimilate for centuries, if ever. Welsh was spoken in Archenfield perhaps as late as the 19th century. And the Cornish, who seem to have lost their political independence by around 900 at the latest, maintained a distinct culture and Brittonic language into the modern era. Some people undoubtedly did migrate away from English rule, but we have to be careful here. For instance, while popular accounts sometimes link British settlement in Armorica (later Breizh/Bretagne/Brittany) to people fleeing the Saxons, it is at least as likely that these colonists went south for a host of other reasons--and that even if they were fleeing foreign invaders, these are more likely to have been the Irish than anyone coming from the East.
As for Christianity, while (as I mentioned) church history is not my strong point, I think it is fair to say that the religion did indeed carry connotations of Roman-ness--at the very least in the person of the Pope, the institution of pilgrimage, and the preservation of the Latin language.
I hope this is helpful, and please let me know if you have any follow-up questions!
