My dna testing (two different) indicated I was 18% Scandinavian. Considering my genealogical research shows near 100% Anglo/Celtic surnames, I’d guess Norse invasions were pretty common back then.
The Michael Wood documentary “The Story of England” (just got it, watched it twice, or rather listened to it and watched it depending on where I was in the house) has quite a bit about the long series of transitions mostly in one small set of villages for which there’s a remarkable paper trail. By the time it fell under Viking rule, the Celts and Romano-Celts had adopted the language and culture of the Angles/Saxons. The roughest period was the Norman Conquest.