Not an essential, this, but something like Doctor Who Live or a Prom or the Doctor Who Experience exhibition. A one-shot adventure with a bigger cast than usual, which doesn't count as part of the series continuity even though it has bits featuring the Doctor and written by the series lead writer.
This could be a convention game, or a game for guest players you know, where the normal players may or may not appear and may or may not play their regular characters - but even if they do, they shouldn't overshadow the guest players. This will need cooperation from the regular players, of course. Otherwise, the game will be rather baffling and full of in-jokes and the guest players may not get to do very much, and all of these are to be avoided.
The guest players' characters are generally normal modern-ish people (as they're easy to relate to) so it's a huge over-the-top space-opera threat looming over normal modern-ish Earth.
It probably features Daleks.
Even if it doesn't feature Daleks, it probably has Daleks appear in a crowd scene of monsters.
L: Hello! I'm the Doctor! And I need your help!
One-shot games are an art in themselves, and one-shot games that also feature ongoing game characters are that bit trickier still. I've done it a few times, and come up with a few tricks to put the new PCs on an equal-ish footing.
If you have a game about modern investigators, have them meet a group of their peers. If one of your regular PCs is a Time Lord or similar overshadowing presence, you could separate that PC from the game in general so that all the PCs have a hand in the rescue which also saves the world. If it's set in a time and place other than here-ish and now-ish, make the regular PCs visitors and the new PCs residents, perhaps with some authority.
Example: Doctor Who And The Shadow Society
The Doctor and Emily, investigating strange sightings that sound like Daleks, Cybermen, Sontarans and Galatea on modern Earth, blunder into a crime scene. A police murder squad will have a lot to say about these two scruffy amateurs getting in the way of their investigations.