It seems to me like the BBC props department said “hey, we’ve still got a load of these android parts from The Android Invasion – can you make use of these again?” and the costume department said “medieval gear, anyone?”, and thus The Androids of Tara was born, perhaps the weakest entry in Tom Baker’s tenure so far.
I do dislike it when alien societies are portrayed as Earth history. It’s the easy way out, it’s lazy, it’s incredibly unlikely too. It’s also hard to believe that a society in which perfect copy androids are a known quantity would not have provisions for dealing with imposters. An android is crowned king, for pity’s sake! It’s also incredibly unlikely that Romana would just happen to look exactly like Princess Strella, who just happens to be the subject for an identical android anyway. I struggle to see the point of that whole setup. The three roles hardly stretch Mary Tamm’s acting skills and the princess spends most of her time in the dungeon anyway.
So, there’s a society that mixes the ancient with the futuristic, in which androids exist, and the concept is wasted on a little game of deception and tricks between the King and the Count. The Count is a terrible villain anyway because he tells everybody all of his plans. When he casually informs Archimandrite that he will wed the King’s widow shortly after his death, I had to wonder why nobody suspected foul play. The sword fight was a weak way to end the story, but it hardly mattered by that point.
And the Key to Time? Yes, it was disguised as a statue for no apparent reason and they collect it before they leave.