By the time written sources show up, the people running things in england are writing in variations on Old English. The fact that we still speak a descendant of this language today indicates its use became widespread, but precisely when and how this happened is difficult to say.

We know, from archaeological evidence, that the im,igration of people from Germany into England in the early middle ages was a slow and ongoing process, not a big invasion like some of the much later written sources claim (ie Bede, the Anglo-Saxon Chronicle). It's very unlikely that the native Romano-British would have been wiped out (archaeological evidence suggests the immigrants mixed in peacefully with the older populations), so there's no simple explanation for why all of England isn't speaking a variant of Latin, or some kind of celtic / Brythonic language, or some language blended together from all three.

We do know that, by around the seventh century at least, English kingdoms were choosing to trace their ancestry more and more to the Germanic sides of their family trees, and it's likely that English became the dominant language through the same processes that led the entire island to adopt an Anglo-Saxon, rather than pseudo-Roman or celtic, identity (like parts of Wales did). Before that, there was probably a lot of regional variation, bilingualism, and local diversity (which, indeed, continued through the middle ages).