The human race has many overlapping ancestries. And is still evolving today. see, just for one example (there are other, even more diverse, theories) : www.independent.co.uk/news/science/human-evolution-africa-multicultural-ethnic-first-people-homo-sapiens-oxford-university-a8442356.html
The British Isles were empty after the last Ice Age. Over the past 10,000 years (approx) the land has been populated by many and different groups of new arrivals. They looked different from each other. They had different beliefs and social organisations and technologies. They were ALL IMMIGRANTS, but, like people today, all were and are entitled to think of themselves as British or English or Welsh or Scottish whatever. Because that's where they lived. At the moment, 'British' legally and politically speaking includes Northern Ireland, Scotland and Wales, as well as England. So citizens in any one of those four branches of the United Kingdom can identify as belonging to one or the other, or both. And/or as European, of course.
In any case, 'white' covers such a vast spectrum with no clear divisions within it. It's nonsense to try to draw boundaries. Some of my cousins have sallow skin, brown eyes and brown hair; others have red-gold hair, blue eyes, white skin and freckles. They are all the progeny of the same grandparents. Appearance tells us very, very little. And it should matter very, very little, as well.
Culture is a different matter - in that it's something we have a choice about. Cultural norms are sensitive, but can surely be managed with tolerance and goodwill on all sides. And, just like physical evolution; they are not fixed. Instead, they change all the time.