You would think that the combination of Doctor Who and the Plantagenets would be a thing of beauty--a good old-fashioned historical, with the Doctor sagely commenting on a key turning point in British history. Imagine William Hartnell, for example, flirting with an aged but still spritely Eleanor of Aquitane.
No, really, he could, dammit; here he is in The Aztecs, striking up a relationship:
Or Troughton, debating Henry II on a fine point of canon law, having been mistaken for Thomas Becket?
No; we get the Fifth Doctor and a suspiciously Monty Python-esque knight duelling for the amusement of a saturnine King John:
Admittedly this bit of dialogue is pretty nifty:
Sir Ranulf Fitzwilliam: "He is said to be the best swordsman in France."
Doctor: "Well, fortunately we are in England."
However, all is not lost; the King (in fact a shape-shifting robot, playing at being a Plantagenet) has a mean way with a lute about him, leading to this little earworm:
(Oh, did I mention that the Doctor--Hartnell again--did meet Richard I in The Crusade? Well, he did, but not as amusing as Gerald Flood singing. Sorry.)