I don't mean German (as in in World War I when the English probably didn't particularly like the German Empire). I mean Germanic. Has the identity of Anglo-Saxon been continuous? Or has there been a time when their ancestry was lost and for it to be rediscovered later?
I dont know if the Anglo Saxons even really knew they were 'Anglo Saxon' in the sense you describe. King Canute called himself King of England, 500 years after Hengist and Horsa came across the channel for an extended holiday, and he was a Dane. If your great great grandparents were a mix of Saxons and/or Angles and/or Britons, how would you even identify yourself? I seriously doubt anyone had even more than a vague idea who they were after several generations in. But there is no clear idea what people thought.
The Anglo Saxon chronicles mention fights between the Saxons and Britons for about 50-100 years after their arrival but this was written long after the event and I suspect some confusion with identities may exist. The first mention of a King of England is 616 and England as a whole in the previous century, altho it seems to be referring to Angles. The problem is that the ASX was written over 300 years after the events it describes, thus it tells us of names and identities as they see it in 900.
So there was always SOME awareness of identity but there is no clear time when or if anyone perceived a transition or change or that they were always aware. The concepts are murky at best, and the evidence completely limited or biased by being written hundreds of years later based on unknown provinance.