“This didn't happen by the way.”
That is the key statement of the episode there.
One of the strengths of “Doctor Who” is that—despite the premise of a man who can go anywhere in space OR time—it is not a show ABOUT time travel. Any story that hinges on the intricacies of time travel is almost surely going to fall apart. Mostly because time travel doesn’t work and is a plot killer.
In this episode the show breaks with its standard form and opts to escapes its cliff-hanger predicament with a time travel cliché. It even breaks the fourth wall and has the Doctor tell us this in the cold-open. That is where the above parenthetical remark is uttered, in the Doctor’s lecture on what a “bootstrap paradox” is.
It’s a shame, really. Because the set-up last week was really good. And, the various elements here are engaging. The creature design is pretty good and there is a call-back to an interesting alien we have encountered before. But none of it really goes anywhere and in the end that shocking imagery in last week’s cliff hanger is simply brushed aside.
In the end, the only important question in this episode is not: “Who really composed Beethoven’s Fifth?” Nor is it: “Where did the Doctor get the list of names?”
Rather it is:
“The Minister of War? No. Never mind. I expect I’ll find out soon enough.”