In related non-news, it's weird how weird it feels to see ESPN ads about the upcoming Champions League final in Cardiff (I did tell you about my how I'm avoiding news channels as much as I can out of psychological self-defense), without making a single reference to Torchwood.
If I were in charge of the BBC, I'd have John Barrowman as Captain Harness be seen briefly during the official transmission; unannounced and unmentioned, doing something vaguely mysterious on the background for a short moment. The parts of the internet you want to know, will see it and pass the word around. Like, in seconds.
Likewise, I'd have every Doctor I can talk into it appear randomly in the background of events, sonicking things, appearing to fix others, just going somewhere else. Turning a corner slightly ahead of a moving camera, and yet not being there when the camera follows. Never giving a heads up, never acknowledging anything. Just have the Doctor, Torchwood, etc, be a random part of the world. You never know where you'll come across the Doctor, and if you're lucky and he's successful, you won't find out what he was trying to prevent.
Hell, if you want to introduce a new Doctor, you just put him in the background of some real events, and then you have bits of his (or her, wouldn't it be nice to dream) episode take place sideways to that event, Rosencrantz and Guilderstein are Dead-style. So, say, a BBC live music event would show, briefly, a guy deliver a music sheet to a pianist, and then months later part of a Doctor Who episode would involve the Doctor replacing a music sheet for a music event with an specific date and place with a deadly tonal harmonic overlay with the proper one, our viewpoint from a side of the stage as he walks to the pianist and gives him the sheet. And the internet would take about thirty seconds to say "hey, that was a real BBC event," and then somebody will watch that video and see a man they now know is the Doctor do the thing right there in reality. Cue, I hope, the yay.
Not that Doctor Who needs any help with the internet, of course. But the BBC, the Doctor, and the United Kingdom might be the only studios, character, and place where you could pull this off in a seamless manner, so why not go for it?
If no British museum ever put Doctor easter eggs in a historical exposition or two and quietly asked somebody's niece to post a photo or two to Tumblr, then I don't know what they think "native social media marketing" is.
Secrets, quoth Hubertus Bigend, are the root of cool.