The prospect of a new King Arthur of the Britons was a distinct possibility (or worry depending how you look at it) as soon as it was known Princess Diana's first child was going to be a baby boy. According to various close confidants of Prince Charles, he had his heart set upon calling the first male Arthur. Obviously this, excluding unforeseen circumstances would have resulted in the first real and official King Arthur.
However this was said to be the only issue Diana adamantly opposed in her first nervous unsure years of being a princess, despite Charles' strong wishes. The child was called William instead.
The possibility of a King Arthur would not have appealed to the Government of Great Britain, as an endless library of allusions would be made to the second heir to the throne's legendary namesake in the media and public conciousness. According to legend King Arthur is promised to return to save Britain from dark destruction in her deepest moment of need. The possibility of a King Arthur being viewed as a noble, flawless monarch whose reign would rescue the nation, instead of a corrupt and incompetent Government would hold no appeal to the defenders of a constitutional monarchy. The perception of being seen to rule over a doomed land that only the King can save would not be appreciated by elected officials.
Looking at the current global and national popularity of Prince William, one can hardly imagine the potential popularity he would have in bringing the Arthurian era of Camelot back to Britain.