You know I think I've pinpointed the exact moment when the left-hand door was first used.
When the show was first broadcast, the Police Box was familiar to the whole viewing public, probably since police films and TV shows set in London would have been shown across the whole of the UK, and dramatic moments would have had characters running for the nearest box to use the phone. So the public knows full well what a Police Box is, and what it looks like. Hence the use of a familiar but incongruous spaceship on the show.
But do they know which doors open? Outside London & Glasgow, probably not, since most drama probably only showed someone using the phone, not going into the box. However, Londoners would most likely know, and the BBC production crew, while not all being Londoners, worked and maybe lived in London, because that's where Doctor Who was made. So they're all familiar with the Police Box too, and make a pretty good effort at making it authentic (even down to the opened windows in "Worlds End").
Now I've not watched a few Hartnell stories, but what I have seen has always had characters entering and leaving the ship through the right door (which the Doctor obviously opens with a key). At no point is the left door used, and I would think this is because a) it would show too much of the inside and b) you'd have the odd Londoner writing into the BBC pointing out how inaccurate it was. I'm not up on Troughton stories either but I've a feeling the same is true, everyone looks out of and uses the single door.
Now we get to the 70s, and Pertwee's still using one door...until 1973 and "Three Doctors".
Right at the end of Episode 1, the Doctor runs out to confront the "gell bridge" and Jo runs after him...and the left-hand door is open and swinging. I think they needed that extra space for the drama of the scene - the doorway has to be wider to allow for the action. That kind of breaks the unspoken rule that the TARDIS only has one door, and from then onwards it's Two-Door-City whenever the plot (or the action) requires it.
Of course if someone can point out a Troughton or Hartnell story where both doors are used, then my theory doesn't hold water. Come to think of it, isn't there a Pertwee episode where he drives Bessie out of the TARDIS? I've re-watched most of Pertwee, and I have a feeling it's in Season 7, but I can't remember which story it is. He'd certainly need both doors open for that, but I kind of remember it was viewed from the side (much like the motorbike cop scene in the TVM, so the doors wouldn't have been visible. I'm off to watch The Silurians now.
