Henry II made it his purpose to have the people realize there was a King Arthur and the Angevins were his descendents. He "rediscovered" the lost tomb of King Arthur and used his "Arthurian descent" to make his campaigns against Wales and Scotland legitimate to the Pope. His grandson, Arthur, was even intended to take the throne as Arthur II.
I think you may mean Henry VII, and it was his son, not his grandson. Regardless, that represents the quirk of a particular monarch, rather than a habitual claim of the British monarchy. It was an attempt to play his Welsh and Cambro-Norman ancestry in his favour, and to style himself as a comparable unifier of and protector of Britain, rather than any assertion of formal legitimacy, such things traditionally being traced to William I. A semi-legendary king, while lending emotive weight to his debated ascension to the throne, was no match for contemporary law and force of arms.
Others instead of claiming descent claimed to be reincarnations of Arthur, James I of England, and VI of Scotland claimed to fulfill Merlin's prophecy of Arthur being reborn. But as Britain turned from Catholiscm to becoming Protestant, he instead started praising his Anglo-Saxon blood.
I've not heard this before, and, frankly, it seems questionable; reincarnation is a belief which any Christian, Catholic or Protestant, would be inherently hostile towards. There is a reason, after all, why the Christianised Arthurian mythology holds that Arthur did not die at all, but lies "sleeping" on Avalon, much like many other Christianised forms of the King In the Mountain motif. I can perhaps see James drawing some comparisons between Arthur and himself, for similar reasons to Henry, particularly given his preference for the legally invalid title "King of Great Britain", but this is merely one eccentricity among many, and from an already rather eccentric king.
Furthermore, James I was a devout Protestant long before the Union of Crowns, and would be unlikely to make claims which had the Catholic overtones you claim, and his rule long pre-dated the Romanticism that raised Alfred to his current status, and at least a generation before the concept of the "Norman yoke" was properly established in English culture. It came into it's own as a reaction to the absolutism and Anglo-Catholicism of Charles and his descendants, but was not strongly pronounced in the time of the more cautious James.
@ Traitorfish: others called Alfred "King of the English", but he himself only ever used the title "King of Wessex" or "King of the West Saxons". It was Athelstan (or maybe Edward the Elder? I'm not quite sure) who actually thought of himself as ruler of a single unified country.
I looked this up; it turns out that Alfred and Edward used the title "King of the Anglo-Saxons", in addition to "King of Wessex", and the title "King of the English" was first adopted by Athelstan. As I said, it was a largely ceremonial title, more of a boast than anything else, but it does reflect the succession of the Kingdom of the English from the Kingdom of Wessex, and Alfred's self-recognition that, while he may not have been the king of all the English, he was, himself, an English king.
