I have a historical linguistic perspective, which is certainly not complete.

Historical linguistics defines a transition from Germanic to Old English, starting around 450-500 A.D. Old English also uses the word "English" or "Englisc," literally "of the Angles."

In 450, the language transition would only just be beginning, with the separation of Old English as a distinct language from Western Germanic being an ongoing process. It is hard to say how fast that development was, since the first written sources of Old English are from ca. 800. We also know that Christianity had a significant influence on its development by introducing Latin terms, starting around 600, that Scandinavian influences began entering the language at ca. 700-800, and that by around 1,000, Old English has reached some limited standardisation.

So from a linguistic perspective, while we do speak of Old English from around 450 onward, it could easily be considered a Germanic dialect then and the distinct linguistic identity of "Old English" was a gradual development over the next 500 years, before the strong influence of French from 1,066 onward began the shift towards Middle English.

Personally, I'd resist drawing a clear line from when I'd consider the Anglo-Saxons linguistically English - they weren't in 450, not really, and they definitely were around 800, after centuries of language evolution and the strong outside influences of Latin and Old Norse. The period in between is one of gradual transition from one to the other.

Bede first uses the term Anglalond and makes reference to a pan-Anglo-Saxon identity in the early 8th Century; naturally his is an Anglalond rather than a Saxolond, reflecting the contemporary Northumbrian political dominance of the British Isles and his own presumed ethnicity. It's Bede who provides us with the narrative of Angles, Saxons and Jutes settling their own respective areas of Britain, although the situation on the ground appears to have been far more piecemeal, which if anything supports a wider pan-English identity.

An actual formalised "English" polity comes into being in the 920s, the result of some 80 years of increasingly close cooperation between Wessex and Mercia, and an extensive campaign of 'liberation' and conquest into former Danelaw territories.