When Dr Who began in 1963, the BBC used the obvious method of naming and numbering shows: the story was given a number and a name as "1- An Unearthly Child", and each episode was given a name, e.g. "The Cave of Skulls." Sounds sensible to me, but apparently not to the BBC. Beginning with story "26 - The Savages" they stopped naming the episodes and just mentioned how many there were. Why? I have no idea, but it's annoying to have to list the episodes as "#1 or #3" just to get an exact date for something else such as a companion arriving.
This questionable technique lasted until story 164 in Christopher Eccleston territory which had two episodes. Now there was no story Name, 164 became "164 - Two Part Story" and the two episodes, "Aliens of London" and "World War Three" now developed names.
So given all that, what happens with a story that has only one episode? Does the story become "One Part Story" and the single episode given a Name? Nope, now we go back to the Story having a Name and the episode being called, "Single episode" or not being there at all.
So, am I saying that the BBC has a few organizationally challenged people working for it? Well, maybe, could be, might be, but there's nothing to be done about it now. We'll just, in Churchill's words, "Keep Buggering On."
Then there's Shada. Shada should have been Story 109, at least it came after Story 108, but the BBC didn't broadcast it so it fell into a limbo where it might have vanished forever, but Tom Baker recued it and made a DVD about two years ago. All good, but where should it go in the list? I decided to put it where it belonged as Story 109 which caused all the following stories to bump up one number, but at least that way the Doctor, the Companions, and the general look of the Story is about the same as the nearby Stories.
And finally, "The Trial of a Time Lord." The BBC had a tiff with Colin Baker, the sixth Doctor and fired him after the 1986 season. I imagine this must have been involved with the peculiar Story numbers in that season. "Trial of a Time Lord was considered to be a story, but it had four stories within it, "The Mysterious Planet, Mindwarp, Terror of the Veroids, and the Ultimate Foe but these weren't episodes, they were stories in their own right and each had their own episodes, 4 in the first three sub-stories and 2 in the last. There had been a couple of other Story situations like this one, "The Key to Time" and "The E-space Trilogy" for two that had sub-stories which in turn had episodes but with those, the big story wasn't assigned a number, but each of the sub-stories was. I decided to use the sensible old method and not assign a story number to "Trial of a Time Lord" (since it isn't a story) and assign Story numbers to the three sub-stories since they are stories. So the story numbers in this list are now 4 higher than the standard BBC list.
The dates. Given stories and episodes aren't shown on the same date by the BBC in London and BBCA in the USA so if you compare a list of Dr Who stories with this list you may notice that the dates are as much as two weeks different. I wonder if the same is true for Dr Who in Australia, New Zealand, etc, I'd guess that it is. The good news is that although the dates may vary, the sequence of the stories is the same so any continuity between stories is maintained.