Near the end, Amy asks The Doctor "So, you have enemies, then?". This is the first part of a famous quote by Winston Churchill: "So, you have enemies, then? Good. That means that you stood up for something, once in your life."
A couple of times, The Doctor flashes a V sign. This is a favorite pose of Matt Smith on red carpets. During WW II, that sign was a V for Victory sign, often used by Winston Churchill himself, among others.
When Mark Gatiss wrote the first draft of the episode, Matt Smith had not been cast as The Doctor. Gatiss wrote this early draft for a generic Doctor, though Steven Moffat commented it sounded like Jon Pertwee and Gatiss agreed. Once Smith had been cast, Gatiss watched Party Animals (2007), as well as anything else Smith was in that he could find. Gatiss used these to "download [his] speech patterns" and examine his energy and phrasing.
This episode holds the record for the most Dalek props (with the exception of CGI, cutouts, toys and other illusions) used in a single story, with no less than eight Dalek models on-screen at the same time.
Churchill's line that "If Hitler invaded hell, I would give the devil a good reference" is an inaccurate version of a remark by Winston Churchill in Parliament in reference to Stalin after Hitler invaded the Soviet Union "If Hitler invaded Hell, I would make at least a favourable reference to the devil in the House of Commons.'
Mark Gatiss: As the spitfire pilot, making this the only episode in which the episode's writer appears on screen.