Not a great deal to say about this one, as we've covered a lot of the background already.
The final part of the Monks trilogy originated with Toby Whithouse's idea for a story based on the sort of totalitarian society seen in George Orwell's 1984. The writer then had to make this act as a sequel, and conclusion, to the previous episodes.
Steven Moffat liked the idea of an invasion that had already taken place - and the Doctor appearing to be collaborating with the invaders. As the darkest iteration of the Time Lord to date, viewers might actually believe that he really had gone over to them.
His role appears to be inspired by Nazi propagandist "Lord Haw-Haw" - William Joyce - whose "Germany Calling..." broadcasts to Britain during WWII were designed to sap morale. He was the inspiration for the villain in Sherlock Holmes and the Voice of Terror (1942). Joyce was hanged for treason in January 1946.
The Doctor appearing to be undergoing a regeneration, but not actually going through with it, had been seen in the cliffhanger to The Stolen Earth, and the Eleventh Doctor had undergone a non-regeneration in The Impossible Astronaut. In the former case, he did use up a life and had to redirect the regeneration energy into a compatible organic receptacle (his hand), whilst in the case of the latter incident it was only a robot copy of the Doctor.
The main element taken from Orwell's novel - written in 1948 and published the following year - was the idea of the Ministry of Truth, which was basically a propaganda machine which presented history as the rulers wished it to be seen, not as had actually taken place.
"Fake news" was a big thing in the media at the time of writing this episode, coming especially from the first Trump presidential campaign where anything negative was dismissed as made-up. It continues to this day.
Whithouse was notified that his episode would be the one where the Vault would finally be opened, and so Missy would feature once again.
It was originally intended that her prison would be a spartan affair. It would be she who would give the Doctor the solution to defeating the Monks, having had previous dealings with them.
The episode opened with a collage of fake history, as presented by the Monks. They would appear in artworks, photographs and newsreel footage, being present at a number of momentous world events as well as appearing in some of the Doctor's own adventures, dealing with Daleks, Cybermen and Weeping Angels.
Moffat had already used this technique to plant the Silents throughout history. Woody Allen had built a whole movie around the idea - 1983's Zelig.
Instead of Orwell's Thought Police, Whithouse introduced the Memory Police - who arrested people who harboured memories of real history.
Having events move on by 6 months from the previous episode, with the Earth already subjugated, reminds us of The Last of the Time Lords. In this, the Master had built a gigantic statue of himself.
A statue which actually acted as a psychic transmitter / receiver was an idea which featured in Douglas Adams' original idea for what later became The Pirate Planet. Then, it was one built by the Time Lords to absorb negative emotions and so pacify a planet's population. A Time Lord sent to dismantle it was caught up in the works and himself absorbed all the negativity, to become the story's villain.
Ordinarily, the Doctor prevents invasions - but having him have to deal with a planet that has already been taken over goes right back to The Dalek Invasion of Earth.
The Doctor's room on the prison ship was described as looking like the one astronaut Bowman finds himself in as an old man at the end of 2001: A Space Odyssey - a stark, brightly lit white space.
The Monk generating thought waves at the heart of the London Pyramid - described in the script as their Cathedral - was to be seen sitting in the pose of Rodin's The Thinker statue (1880).
Next time: Zulu, but with Ice Warriors...