The Irish and Scottish are Celtic, not Anglo-Saxon. They are linguistically and culturally Celtic but are related to the Anglo-Saxons because they all derive from the same Indo European people.

The Irish and Scottish have a heavy Genetic relation to Anglo-saxons due to the settlements in Ireland and Scotland

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Anglo-Saxon

Roger H. White has written:

'Roman and Celtic objects from Anglo-Saxon graves' -- subject(s): Anglo-Saxons, Celtic Antiquities, Funeral customs and rites, Roman Antiquities

No, King Arthur is not believed to have been an Anglo-Saxon. He is a legendary figure from Celtic mythology and is associated with the Britons, who were a Celtic people. The Anglo-Saxons arrived in Britain centuries after the time when King Arthur is said to have lived.