The audience for the Christmas special of Doctor Who – which is likely, as always, to reach many millions – will include one particularly interested viewer: Peter Capaldi, who plays the Time Lord himself.

But the actor, who has been widely acclaimed for his magnetic performance as the 12th incarnation of the Doctor, admits that he will be switching on with some reservations.

Capaldi, who is teaming his trademark “electric shock” hairdo with a smart dark suit today, explains why. “I have always watched Doctor Who at Christmas, even before I was involved. I still do, but now I watch it from behind the sofa because I’m terrified of my acting and my hair! But it’s still the centrepiece of our day. I wouldn’t like to deprive my family of that.

“Doctor Who should be on Christmas Day. It suits Christmas. It’s a little bit scary, a little bit nostalgic and a little bit festive. Christmas should be really scary. It is in my house, but I think we get it mixed up with Halloween.”

With a presence as vivid and electrifying as his hair, 58-year-old Capaldi makes for compelling company. He possesses an unusual, almost otherworldly charm that makes him perfect for the role of Doctor Who. A lifelong fan who famously wrote to the Radio Times as a young boy praising the programme, the actor brings a rare relish to the part.

A live wire with a captivating use of language, Capaldi manifests a very appealing sense of humour, too. When asked, for instance, if he gives people Doctor Who gifts for Christmas, the actor replies, “Not unless it’s someone I know loves Doctor Who. Otherwise, I give people personal gifts.

“Obviously, I could show up on Christmas Day, and all my relations would say, ‘Uncle Peter has given us a Doctor Who calendar.’ But if every relative of mine had a Doctor Who calendar, it might pop into their heads that a job lot of them had been supplied to me.”

In a similar vein, Capaldi talks about the classic Doctor Who injury that he has sustained this year. “I have got the same knee injury as Matt Smith [the actor who played the last Doctor]. When I first met him, he came hobbling into the restaurant on crutches. I said, ‘What’s happened to you?’ ‘It’s the show, mate’.”

Capaldi, who has now played the Time Lord from the planet Gallifrey for the past three years, proceeds to stand up and demonstrate the action that has caused such trouble. “I’ll show you.

”You run down the corridor, reach the end, and then spin on one leg to make sure you get a nice close-up. But when you spin, you put tension on that knee and that’s why it hurts. We should come up with a name for that injury. How about ‘Gallifrey Knee’?”

The actor will surely only have exacerbated his already serious case of “Gallifrey Knee” in playing the Doctor in “The Return of Dr Mysterio”, this year’s Christmas special, which goes out at 5:45pm on Sunday.

In this episode written by showrunner Steven Moffat, the Doctor travels to New York, where he teams up with an enigmatic superhero known only as The Ghost to tackle fiendish, brain-swapping alien baddies bent on world domination. Will the Doctor manage to save Manhattan?

The actor, who also made a huge impact in a previous leading role as the foulmouthed spin doctor Malcolm Tucker in Armando Iannucci’s multi-award-winning political comedy, The Thick of It, tries to recollect if he has ever been responsible for an act of heroism.

With a wry grin – he does a lot of wry grinning – Capaldi recalls that, “I once turned the woman next door’s water off when she had a burst pipe while she was out. I had to put my hand down a hole in the pavement. I know nothing about plumbing, and there was just water gushing everywhere.

“Her house was flooding fast, so I thought, ‘There is obviously a thing you turn down there.’ But I wasn’t sure what I would find. There could have been a monster with teeth down there. It was at that moment that I thought, ‘Maybe one day I’ll play Doctor Who.’”

But further than that, Capaldi does not discern any similarities between the Doctor and a superhero. “I don’t think Doctor Who and a superhero have much in common,” muses the actor, also a very accomplished director who in 1995 won an Oscar for Best Live Action Short Film for Franz Kafka's It's a Wonderful Life.

”Doctor Who is a sort of anti-superhero. He doesn’t have tights, as far as we know. But I’ve got them. I wear them under my trousers! The Doctor is not as slick as the traditional superhero. They don’t really come from the same place – or do they?”

Moffat, 55, chips in that, “Superheroes specifically say they are heroes, but the Doctor doesn’t ever do that. He is more of an accidental hero. He is just larking around in time and space.”

Doctor Who may not be a superhero, but this episode certainly chimes with the tone of the earlier, less earnest superhero movies. Capaldi observes that, “There is a lovely wit to some of the movies.

“For instance, in the early Christopher Reeve Superman movies and the old Batman episodes with Adam West, there is a tremendous tongue-in-cheek humour about the whole thing, which has slightly vanished from the world of superhero movies now. But that tongue-in-cheek element is there in this episode.”

All the same, Moffat is quick to point out that “The Return of Dr Mysterio” does not send up superheroes. The showrunner, who is also the co-creator of one of the BBC’s other immense global hits, Sherlock, declares that, “You can’t take the mickey for very long. Even five minutes is pushing it. You’ve really only got a sketch then. You have to tell the story sincerely.

“We’re trying to tell a good superhero story and have fun with the idea of a superhero, which mainly comes from the fact that they have to have a secret identity. That means that shy, socially awkward people can believe that at some point they could become a god – which is something I’ve always clung to!”

With its legions of adult fans known as “Whovians”, there is always a debate about which audience Doctor Who is appealing to. But Moffat, who also created the award-winning children’s drama Press Gang, remains adamant that the show should first and foremost speak to younger viewers. “I always say it’s very important to appeal to children. You have to be able to draw the monster. We talk a lot in script meetings about, ‘What is the playground game?’

“That doesn’t mean we take it simply. Doctor Who stories can be complicated and emotional – you’re supposed to sit up and watch it. But you have to keep in mind the slightly different, more intense, more emotional way that children watch TV. At its heart, Doctor Who is a children’s programme that adults absolutely love. Ultimately, it belongs to children. There isn’t a Holby City lunch box – or if there is, it’s not selling very well.”

Hitting his rhetorical stride now, Moffat asserts that, “I feel very strongly about this. Just because Doctor Who is a children’s programme, it doesn’t mean that it’s dumb – in fact, quite the opposite. Children’s TV has to be challenging. You have to stay ahead of the audience because, let’s be clear, kids are smarter than us – and that’s why we don’t like them.

“Doctor Who is a good-hearted adventure where the adults say, ‘This is a really clever show’, and the kids say, ‘Yes, but it’s ours!’ It fills that slot. We can all sit down and watch it. I always think Doctor Who is like when you go to a restaurant and glance longingly at the children’s menu. You think, ‘That’s so much better than the risotto I have to pretend I want.’”

Moffat has announced that he will be stepping down from his role as showrunner at the end of the next series of Doctor Who. Is he already beginning to feel sad about his impending departure? “No. That would be pre-emptively wistful, and I don’t think you can do pre-emptively wistful. But I’m sure I’ll be bitter when it’s over. I’ll say, ‘Why did it end?’ ‘Because you left, you idiot!’

“So I don’t feel wistful yet, but I’m sure the day is coming where I’ll be writing an angry piece for a broadsheet newspaper about how the BBC has lost its way and my phone number and how things were better back in the day. I’ll do that the day after I’ve left!”

One thing Moffat promises he won’t be doing is making a valedictory, Hitchcockian appearance in an episode of Doctor Who. “I’m the executive producer, and I can stop things like that happening because I know I’m a very, very bad actor. It would spoil Doctor Who for me.

“I’d be watching and thinking, ‘Oh no, not him. He can’t act!’ I was in an episode Peter Davison made called ‘The Five Doctors’ playing myself, and even that proved to be out of my range.”

Before we part, Capaldi reflects on whether he has nailed the role of Doctor Who yet. “I don’t think I have, but that’s the way you should be with every part. I find it surprising when actors say, ‘I’ve nailed it. I know how this works.’ I don’t know how it works. I just keep going. It’s clear after a while that certain things are more popular than others, but it would be a mistake to say I know how to do something.”

But does this childhood fan of the Time Lord still get the same joy as ever from playing the part? “Of course! It’s Doctor Who, for goodness sake! What’s not to like?”