Some time after ending his time travel campaign with The War Games, the GM proposes a new one. This will be about a semi-secret military organisation dedicated to protecting the Earth from alien invasion and investigating the downright weird. He initially gets three players for this new campaign, and they set out about creating suitable characters.
One brings back the Doctor, from the previous campaign, but now suitably changed with the addition of some nifty combat skills and, of course, no time machine. (Maybe the last episode of The War Games is actually a flashback worked out to explain this, or maybe it was planned all along, when the GM got bored of running games about time travel and future worlds).
The second player also brings back a character from the previous campaign, but this time, it's a former NPC. This, of course, is the head of the British branch of UNIT, Brigadier Alastair Lethbridge-Stewart. (The middle name 'Gordon' isn't added until quite a bit later).
That the Brigadier was originally an NPC seems fairly evident. He first appears (as a colonel) in The Web of Fear, in which he is one of the main suspects in the whodunnit sub-plot. Crucially, he is treated as such by the regular characters pretty much all the way through, and they don't start to trust him until the true villain is unmasked, right at the end. Therefore, I would argue, the players are treating him as they would any NPC suspect. Yes, he's a red herring, but they don't know that, and they aren't treating him like a fellow PC.