"Go on, my sun!"
The End of the World: Companion gets superphone from the Doctor and rings her Mum, pretending that everything is normal as she does so.
Aliens of London: Companion gets key to TARDIS as mark of status with the Doctor.
Dalek: Human illegal/amoral action triggers chase scene with unstoppable enemy in closed environment.
The Impossible Planet/The Satan Pit: In the Radio Times, Chibnall acknowledges that these were "an influence," though perhaps "straight ripoff" might have been more accurate (did I say "straight ripoff"? I meant "generous homage"). Far-future multiethnic space-faring human culture in postindustrial setting where everyone walks around sweating in grotty workwear; mysterious voice speaks to, then infects and takes over, buff male crewmember, who then goes around being all sinister, having funny eyes, and repeating catchphrases; Doctor makes remarks about indefatigability of humans; the Doctor becomes separated from his companion, who nonetheless trusts that he'll rescue her somehow; the Doctor and companion are separated from the TARDIS, with seemingly no way to return, early on; the pretty/young female crewmembers are dispatched quickly, while the companion hangs out with male/working class ones; Doctor suits up for journey into the unknown; the bit where McDonnell and Korwin go floating balletically off into space is far too similar to the one where the dead Skooti drifts off to the black hole.
Fear Her: Fraught suburban Mum/daughter relationship; shadows being burnt/drawn into walls.
Earlier This Season: What the hell is it with Season 3 and MRI machines?
Timelash Moment: Seemingly dead villain-monster revives.
The Fifth Element: Gritty working-class-sci-fi with nonetheless beautiful space sequences. Colour scheme heavy on the reds and yellows.
Old Skool Who: Pretty much any of the base-under-sieges, particularly if they involve aliens taking somebody over rather than invading from outside (The Invisible Enemy, The Wheel in Space, and see below); also any of the Robert Holmes man-gets-infected-with-something-that-takes-him-over-to-the-dismay-of-his-relatives ones (Seeds of Doom; Ark in Space; Pyramids of Mars). Resurrection of the Daleks and Earthshock (Alien-influenced post-industrial chase stories with tough women leaders; at least two homages to Resurrection's "does nothing work properly?" moment); Destiny of the Daleks (twitching-hand revival); Terror of the Vervoids (the facemasks; the colour scheme; the murder-on-a-spaceship theme); "The Pyramids of Mars" (seemingly human villain, actually taken over by some sort of alien; baddie who can cause people to steam to death by touching them, and has a sinister calm voice; bit where the sibling/partner of the taken-over person attempts to bring them back to themselves by reminding them of the relationship, with no success); "The Invisible Enemy" (Doctor taken over by alien and urges his companion to try and cure him; infected people walking around in helmets with visors, opening them up to reveal their infected state, and zapping other people with their eyes, as well as muttering catchphrases); "The Stones of Blood" ("Where's that Dunkirk spirit?"); "The Daleks' Master Plan" (character ejecting herself and another character out the airlock to save the others); "Planet of Evil" (planet/sun is actually alive and taking people over, picking off crewmembers one at a time, and appeased when something taken from it is returned; people with glowing eyes).
Outside Sources: 24 is the most obvious one (realtime, or supposed realtime in the case of 24, action; action-adventure style, and government conspiracies), but you can also take your pick of the 1980s sci-fi-with-dirt-and-bugs-in boom (Alien and sequels/ripoffs, Event Horizon, even Star Wars usually shows the dings and scratches on the droids; this just makes RTD's proud claim on "Confidential" that this is somehow uniquely British rather silly-sounding). Alien and sequels/ripoffs also major source for McDonnell (working-class woman spaceship captain running around being tough in a singlet); The Black Hole (crew of spaceship about to crash into a natural phenomenon and trying to avoid it). Star Wars (compare the bemasked and gasping villains to Darth Vader, and watch George Lucas choke on a hobnob and phone his lawyer). Solaris, particularly/exclusively the film with George Clooney (planet/sun which is a living entity, driving people on a spaceship/station above it mad; the bit where Martha is shot into space in an escape pod is visually very close to the scene where Clooney's character deliberately shoots "his wife" into space similarly). Twin Peaks ("Fire walk with me"). "Last of the Mohicans" (RTD admits to this one: Daniel Day-Lewis' "I'll find you" moment). Red Dwarf (gritty, working-class, eighties, post-industrial etc.; character in stasis chamber). The Old Men at the Zoo (shadows burnt onto the wall; plus pick any documentary/drama about Hiroshima/Nagasaki); Not sure if Saxon's minions are closer to The X-files or The Men in Black.