Old English Angli Saxones (plural), from Latin Anglo-Saxones, in which Anglo- is an adjective, thus literally "English Saxons," as opposed to those of the Continent (now called "Old Saxons"). Properly in reference to the Saxons of ancient Wessex, Essex, Middlesex, and Sussex.
I am a suthern man, I can not geste 'rum, ram, ruf' by letter. [Chaucer, "Parson's Prologue and Tale"]
After the Norman-French invasion of 1066, the peoples of the island were distinguished as English and French, but after a few generations all were English, and Latin-speaking scribes, who knew and cared little about Germanic history, began to use Anglo-Saxones to refer to the pre-1066 inhabitants and their descendants. When interest in Old English writing revived c. 1586, the word was extended to the language we now call Old English. It has been used rhetorically for "English" in an ethnological sense from 1832, and revisioned as Angle + Saxon.