Doesn't the English monarchy claim lineage back to David?

No, they don't. But they do claim lineage to Alfred the Great, whose lineage is traced by legendary sources to Woden/Odin, and from there to Noah and Adam. In some versions, Beowulf is also part of that lineage.

	▲	dylan604 27 minutes ago \| parent [-]
		Okay, so maybe the family doesn't but others do. There's the Davidic throne concept people believe that does claim that lineage exists. These are usually religious types though.