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Apparently the last member of the Anglo-Saxon royal line, Edgar the Aetheling who at 15 was not elected to the throne by the Witanagemot made an appearence during the First Crusade. He was commanding a fleet apparently crewed by Anglo-Saxon exiles and put in to St Symeon to land Italian pilgrims and seige equipment and then marched on Lattakieh but couldn't leave a large garrison.
Is there any way this could be morphed into the Anglo-Saxons getting a state in Palestine? If Edgar is there in charge of a fleet crewed by AS exiles and the Varangian gaurd is full of AS exiles perhaps they could grab something for themselves with a few shifts of fate.