As a brand, the show is so successful, internationally, that surely no amount of Tardis-building could break its bank? “It’s complicated: it is a brand, so it has to be sold. But the actual spirit of it is quite personal and small. So you have to look after that a bit, but also go and be a salesman for it.

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“I go on tours with the show, and if you go to South Korea, Australia or South America… In Mexico, the fans were just so wonderful, and passionate, and… Latin!”

The intensity and spread of international fandom took a bit of getting used to. “I found it hard at first. You walk on stage and it makes people go crazy, not because you’re me, because you’re Doctor Who. When you see little kids, that’s fantastic. A wee bit like being a mythical character, like the Wizard of Oz or Santa Claus.”

Famously, when Peter Capaldi was announced in the role, a fan letter came to light that he’d written to RT in 1974 aged 15.

It seemed like a perfect alignment of the stars, the ultimate human fulfilment, that an actor could become the hero of his youth. It annoys him a bit now. “It makes it sound as if I spent my life, my career, grieving that I wasn’t the Doctor. Which is not the case,” he says stoutly. “As a kid I loved the Doctor, but as a teenager I moved on, and discovered sex and drugs and rock ’n’ roll like everybody else!”

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As a graduate of the Glasgow School of Art, Capaldi honed skills that he retains to this day, as shown in his artwork for this very feature (see how you could win it here). The role of the Doctor is such a consuming one that it’s easy to forget what he was famous for before: that splenetic, hyper-intelligent energy he brought to the screen, most memorably in the BBC’s painfully good satire, The Thick of It.

Yet it’s not as though he’s moved into “family entertainment” as such. Doctor Who has become more and more cerebral, or certainly, less and less easy to explain to a nine-year-old, unless you’re really concentrating.

“The thing about Doctor Who is the constitution of the audience. It covers a huge age range, so you have to entertain little kids and you have to entertain hipsters and students, and middle-aged men who should know better.

“So sometimes there is a kind of metaphysical and intellectual aspect to it, which is more to the fore than other times. But generally we just blow up monsters. There are some moments when you feel, that’s a little bit silly, or that’s a bit mawkish or whatever, but then you realise, that’s for children. You would be a fool not to play to them, because it’s their show.”

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The studio is empty of action but Capaldi is speeding down the obligatory Doctor Who corridor then spins round to show how he injured his knee last year. “When I first had lunch with Matt Smith, he arrived on crutches. I said, ‘What happened?’ and he said, ‘This show, this show.’ I thought, ‘My God, he’s 14, and he still injured himself.’ ”

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