Yes I could perhaps have been more careful how I phrased the starting post. According to
Wikipedia, 97 of the 253 episodes from the Hartnell and Troughton years are still missing, although the audio from all episodes still exists, and many of those episodes have been recreated as animations with the original audio. In fact, episode 3 of Web of Fear is one of them, so what I watched on iPlayer was the entire Web of Fear story, but with episode 3 animated. Not nearly as much fun to watch the animated bit, but not too bad if it's only a single episode.
So I guess in actuality, what's on iPlayer is: All stories from Jon Pertwee onwards (except if I recall correctly, I think one episode of Invasion of the Dinosaurs is only available in black and white), and most of the Hartnell/Troughton episodes, with some animated only.