Karen Gillan is coming home. A couple of weeks back, she announced on her Twitter feed that despite having “a small mountain to climb” she’s heading back to Scotland for Christmas and Hogmanay. Cheekily, she began the tweet: “Hide the Buckfast.” While the Scottish star of Marvel's Avengers film franchsie undoubtedly advocates drinking responsibly, you can’t deny her a little festive tonic wine tipple. After all, this has been a year for celebration.

Never mind that Gillan has just turned 30, the vibrant redhead has been storming the Hollywood battlements with a vengeance. When we meet, she’s still embroiled in shooting the superhero ensemble Avengers: Infinity War and its as-yet-untitled follow-up. “I belong to Marvel for the rest of the year,” she says, smiling. The 12-month, two-film shoot – one of the most expensive movie projects in history – will see Gillan reprise her role as Nebula, the blue-skinned alien she played in Guardians of the Galaxy and this year’s Vol 2 sequel.

After travelling the galaxy as Doctor Who’s companion Amy Pond, her breakthrough role, Gillan now gets to hang out with the likes of Thor’s Chris Hemsworth and Iron Man’s Robert Downey Jr. Understandably, she never planned it this way. “I didn’t think it was a plausible thing,” she says. “Also, the crazy thing is when I first signed on for the role I thought it was going to be eight days of filming. I thought the character was going to die. Now five years later I’m in the Avengers.”

While all that spandex is undoubtedly mind-blowing – she lets out a big “woah” as she says it – she’s also made her directorial debut with The Party’s Just Beginning, a film that brought her back to her native Inverness. To top it all, this Christmas she stars in a remake of the 1990s big-screen adventure Jumanji. “I love the original so much – it’s in my top three films of all time,” she says with unbridled enthusiasm (to be fair, she was seven when it came out).

Perhaps it's fate that Gillan should be chosen to play in a remake of a beloved film, which starred the late Robin Williams. “When I had an audition for it, I couldn’t understand it,” she says. “I was like, ‘What? What are the chances of this?’ And then I was like, ‘What are they going to do with it?’ I was immediately protective over it.” She read the script and was relieved. “It was just legitimately so funny. It has its own identity; it hasn’t stuck exactly to the formula of the first film.”

Unlike the original, which saw a magical board game unleash carnage in the world, here four teenagers get sucked into a jungle-set video game, each becoming their selected avatars. In Gillan’s case, she’s the high-kicking Ruby Roundhouse, who is transported into the undergrowth in micro-shorts and a crop-top. “We all have our special skills, and we’re trying to learn how to use them, but we’re also four dysfunctional teenagers that can’t get along with each other at the same time.”

She co-stars with comedy giants Jack Black and Kevin Hart, and also Dwayne "the Rock" Johnson, the former pro-wrestler turned highest-paid actor on the planet. Did she get to use the private gym – what he calls his “iron paradise” – that comes with him to every movie shoot? “I did not use his private gym, because I think he uses it at five in the morning, and I am not getting up to do that,” laughs Gillan, making the sort of down-to-earth comment that immediately endears you to her.

An athletic 5ft 10in, Gillan’s long-limbed physique was once likened to a preying mantis by her Doctor Who co-star Matt Smith (he also dubbed her “the sexiest companion ever”, after making her debut on the show as a kiss-a-gram dressed in a policewoman’s uniform). Gillan shrugs at the idea that she’s become a sex symbol among the legions of Marvel and Doctor Who fans. “It doesn’t feel like a massive achievement,” she giggles. “But it doesn’t feel like the worst thing I’ve ever heard.”

Splitting her time between New York and Los Angeles, Gillan is now at a point where it’s becoming harder to go unrecognised. When she and Smith visited DragonCon – the second biggest fantasy convention after the San Diego Comic Con – they took to the floor in disguise. “We decided to get some weird gimp-looking masks. I don’t know where they came from. And I don’t want to know. But we put them on with some hats and walked around and it was so much fun. And nobody recognised us.”

She’s still very much associated with Doctor Who, despite leaving the show five years ago. With Jodie Whittaker about to become the show’s first female Timelord, Gillan is hugely excited. “I’ve been waiting for this moment when a woman gets the role and it’s finally happened. I just know she’s going to be amazing. She’s such a good actress.” Will it be different with a woman Doctor? “I don’t think it’s hinged on the gender,” she says. “But it’s going to be different. We’re going to feel it at first.”

Perhaps the most satisfying development for Gillan is making her directorial debut with The Party’s Just Beginning, whose screenplay she also wrote. Set in the Highlands, the story is about a girl called Lucy, played by Gillan, whose best friend has just taken her own life. “She’s suffering all of the stages of grief and blaming herself and [feeling] guilt and shame and all of these things, so she’s quite self-destructive throughout the film. It’s about her trying to overcome that.”

What drew her to such an emotional and tragic topic? “It’s not something I’ve personally experienced. It came from a statistic where the suicide rate was higher among men in the Highlands than anywhere else in Scotland, and I was like, ‘Why?’ I think it’s been voted the most idyllic place to live in the UK. It’s beautiful. And it’s such a lovely place to grow up, so I just started to wonder why that was. That led to me writing the script.”

Making the film brought her back to her youth – and not just because of shooting around Inverness, where she grew up. “The first time I ever got into acting was when I got a video camera, and I started writing and directing little horror films around my house, where I would end up killing my dad.” She chuckles again. “So it was really fun. We would get tomato sauce and use it for blood, and everything. And so I’ve actually been doing this since I was a kid.”

The only child of Marie and Raymond, Gillan was a natural-born performer. Singing came first. “My dad’s a massive music fan, so I was always subjected to Ella Fitzgerald, Nina Simone, Elvis Presley and Frank Sinatra, people like that. That was my first love.” The Spice Girls were also big in her life (“Ginger Spice, obviously”), and Gillan learned to play the piano by the age of seven (there’s a lovely shot on Twitter of her playing piano with her Jumanji co-star – and former pop sensation – Nick Jonas).

Acting arrived later, after trying out local drama clubs, although Gillan was obsessed with the Disney cartoon Alice in Wonderland from a young age, and desperately wanted to be Lewis Carroll’s heroine. “I still do. I’m going to call my daughter – if I ever have one – Alice.” By her teens, she was rampantly daydreaming about another life. “I remember really hating being in school,” she says. “I used to sit in fashion class in school and I’d sneak off and go and look on the computer for auditions on The Stage website.”

Gillan soon discovered an acting and performance course at Telford College in Edinburgh. “I thought: ‘I’m going to go down there and get out of school.’” Accepted, she left home and within a year she was off to London to continue her training at the Italia Conti Academy. What did her parents think? “My dad and my mum have always had the view that I should be able to do whatever I want, in terms of my career. So they always supported me. But I think Dad was quite worried when I moved down to London at a young age.”

Headstrong and independent, Gillan quit the course when she was 18 so she could shoot eight days on the TV adaptation of Ian Rankin's Rebus novels. Rather than lament this rash decision, she took up waitressing and working in a London pub. “I think that was really important for me. That’s the reality of it. You get a job here and there and you have to really try to get into acting, unless you’re very lucky of course. But also to just work in a pub and do that kind of job, I think it’s important to experience that. I can appreciate this all the more.”

Gillan also got scouted as a model. Much later on, she got to live out that fantasy, playing Jean Shrimpton in TV movie We’ll Take Manhattan, but at the time, it was a means to an end – to support her while she was doing auditions. Better paid than working behind a bar, perhaps, it still represented thwarted ambitions in her mind. “I always resented the fact I did modelling. I just associated it with not doing acting. If I was doing modelling that meant I wasn’t acting.”

Soon enough she was playing bit-parts on television dramas before winning a two-year gig on the sketch comedy series The Kevin Bishop Show, impersonating the likes of Angelina Jolie and Katy Perry. The real life-changer came with Doctor Who, allowing her to quit modelling for good. Paparazzi descended on her, camping outside her flat and snapping her from inside their cars. “That was quite extreme at the beginning, and I remember being like ‘What?’”

At the time she was dating photographer Patrick Green, a six-year relationship that ended in 2015. As she told one newspaper last year, moving to America has made navigating the dating scene all the more complex. “Americans seem to go about it in a different way, where they date loads of people at the same time. It’s probably a healthier way of finding someone, because you don’t put all your eggs in one basket. I prefer the UK way, where we just drink near each other and no-one knows if it’s a date or not.”

For the moment Gillan is too busy for love, finishing off Avengers: Infinity War, which was partly filmed in Edinburgh. “I can’t wait to see those scenes because I don’t even know where they shot,” she says. So she didn’t get to shoot there herself? “No. And I’m the only Scottish person in it … It was so funny, some of them even went up to Inverness for a holiday, and met people I used to work with in a pizza shop.” The Avengers ordering the pepperoni special? Pass the Buckfast.

Jumanji: Welcome to the Jungle (12A) is in cinemas from Wednesday