A subset of The Big Two-Parter, and worth going into detail over because a lot of Big Two-Parters are Secret Invasion stories and they're different enough from a regular Aliens Of London story to have their own common features.
Modern Britain (or some similarly recognisable culture) is threatened by sinister forces working in secret in part one, and then more openly in part two.
Another of the classic Who adventure models, largely lifted from Quatermass II. So, in that spirit, I'll be lifting a bit from the DWAITAS forum post by sutekh which inspired this entire series of articles. ;)
(Look at the rest of his story type rundowns while you're there, I won't be covering them in their own posts but they're all gold dust if you want to run something like them.)
7: What's going on?
Doctor Who can afford to do overt alien invasions nowadays, but still tends to prefer a bit of sneaking around before the invaders reveal themselves fully. This generally involves strange phenomena that the travellers can investigate, possibly human proxies working (possibly unwittingly) to advances the invaders' cause, and the audience knowing perfectly well what the aliens are by seeing "meanwhile" cut scenes or even reading the episode title.
Strange phenomena tend to start small, like unusual weather patterns, funny readings or odd meteorite strikes. Just enough to provide initial clues, and point the travellers towards the central point of the events which will be the invaders' landing spot.
However, this category can also include spaceships crashing into Big Ben and massive numbers of blurry ghosts strolling around all over the planet. The really big early phenomena are usually tricks or distractions from the real plan, but have some clues that will lead the PCs to those behind the scenes.
Human proxies might be profiteers, dupes, mind-controlled slaves, or fake humans such as shapeshifting aliens or Auton duplicates. They give the characters someone to talk to and be suspicious of right away. Real humans might realise the error of their ways or throw off their control (and die making up for it), while fake humans may be too well-programmed and have a spark of humanity that the characters can use to turn them to the good and probably again lead to heroic self-sacrifice.
In a modern setting (the default for a secret rather than overt invasion) strange phenomena will generally attract the attention of UNIT and other bodies, who will help or hinder the travellers as required, and include a decent number of particular NPCs for the PCs to bounce off like the by-the-book officer, the down-to-earth squaddie and the head-in-the-clouds academic. Some of these characters will die to show how the monster works. Others may become much-loved recurring characters, even part-time companions.
The invaders need a way to sneak in, which can spread quickly to threaten the city/country/world as a whole. This could be something nobody notices or something everybody wants.
The alien threat may be connected to modern concerns (food shortages, the spread of consumer culture, the oil crisis, pollution and global warming) but it doesn't have to be. Plans to steal the Earth's magnetic core or eat everybody on the planet are perfectly acceptable too.
I mentioned Quatermass above because, as noted, the Secret Invasion became a standard in the Pertwee era and there was a lot of self-conscious borrowing from Quatermass II in particular, starting with his first story Spearhead From Space being a partial remake with the addition of killer shop window dummies.
Speaking of which, I'll steal the next bit of text directly:
"Classic Doctor Who invasion stories are usually built around an iconic moment when the nature of the alien threat is openly revealed - the Cybermen emerge from the sewers, Auton dummies smash through shop windows, etc. These moments typically occur quite late in the story. In a four-part story, they tend to occur towards the end of episode three and in a six-part story they tend to occur late in episode four or early in episode five. The reason for this is pacing - once the alien menace is openly revealed, the story needs to move briskly towards the climax.
The third episode usually ends with the moment when the alien invasion is openly revealed. This is the iconic moment that people tend to remember - Cybermen on the steps of St. Paul's cathedral, Autons coming to life in shop windows, etc. It is worth putting a bit of time and effort into the moment where the alien menace is revealed - try to come up with a strong visual image that communicates the immediacy of the threat to the players."
So be sure to include a "there they are!" moment, ideally as an end-of-session cliffhanger. And make it awesome - this is the moment that would turn up in clip shows and Doctor Who Confidential for years to come.
While The Sontaran Stratagem reveals its eponymous stars early on, Army Of Ghosts plays its cards a lot closer to the chest and only shows who the Ghosts really are and what's inside the Sphere right at the end. They even managed to keep it off the cover of the Radio Times, instead giving both sides covers next week instead. It was that big. (It was also a Season Finale, so we'll come back to it later.)
Example: The Furies / Black Fire
The travellers return to modern Britain to find a fuel crisis under way. The modern companion's friends and family are queuing up outside the petrol station, while that guy with a hybrid car is saying "I told you so" while also keeping to the electrics. This could be normal, but it seems to have come up rather suddenly... because someone has been siphoning oil away from wells, drills, and reservoirs. The stealth ships of the vainly cybersculpted Galatea need oil to make plastic, with which to rebuild and revive their sleeping cybernetic armies and conquer this world and more like it. The big cliffhanger sees the travellers trapped on an offshore oil rig as a swarm of fighter spacecraft decloak all around it, with beautifully masked cybernetic pirates abseiling down to take over!
(This one is pretty tricky to get right. I rejected an idea about Ice Warriors reversing global warming for being too much like The Sontaran Stratagem, one about electricity monsters causing storms because they had no strong reason to, and one about a medical miracle for being a potentially too-horrible non-funny version of Partners In Crime, even though the bad guys were vampire doctors and nurses. Finally, I borrowed the way off-model but interesting idea for the Cybermen from the attempted 1990s Doctor Who revival, cyborg pirates with a thing about their looks.)