OT: Of Angles and Saxons

I recently ran across the claim that no Anglo-Saxons called themselves 'Saxons'
before the Conquest - that is was strictly an exonym - but all considered
themselves Angles/English. The names of kingdoms and regions containing "Sax" -
Wessex, Sussex, Essex, Middlesex - supposedly all postdate the Conquest, and
were introduced by the Normans (leaving one to wonder what the kings of Wessex
and so on called their kingdoms).

I find this more than a little difficult to believe, but couldn't find any
explicit denial in any book I've got easy access to. Anyone into these matters
feel like commenting?

                                               Andreas

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