Terminator role for Thrones star

It's the sort of down-to-earth admission that typifies this hugely likeable 28 year-old Brit. Stripped of the blonde wig she sports to play Daenerys, with her brunette shoulder-length locks, she's almost unrecognisable from her work on the HBO fantasy drama. Which has meant, so far at least, she's flown "under the radar", with fame "unobtrusive" in her personal life. Typically, it's at the most random moments that a fan clocks her - usually running after her pooch. "I'll be walking around, picking up dog poo or whatever, and someone will be like, 'Can I take a picture?'"

Still, that could all change with the release of her first major Hollywood movie, Terminator Genisys. Starring with Arnold Schwarzenegger, who returns to his signature role as the T-800 cyborg killing machine, Clarke plays Sarah Connor - the character immortalised by Linda Hamilton in the first two films directed by James Cameron. So is she expecting her anonymity to be eroded? "I don't know," she sighs. "I'm so different from Sarah, energy wise...I'm not walking around with my gun and my Doc Martins!"

This latest instalment returns us to 1984 Los Angeles - the setting for the original Cameron movie The Terminator - with a head scratching plot involving alternate time-lines, multiple Terminators and frequent twists. Reuniting Clarke with director Alan Taylor, who previously helmed episodes of Thrones, she makes no apologies for the story's wilful complexity. "[We're] forcing people to use their minds. Which, as a Terminator fan myself, was what I liked."

Unlike the 1984 original movie, where an unwitting Connor is pursued by Schwarzenegger's Terminator - sent back from the war-torn future to kill her before she gives birth to resistance leader John Connor - Genisys sees her protected by a T-800 since childhood. It gives the film a father-daughter relationship, unseen in the earlier movies, which Clarke admits was replicated in her time on-set with Schwarzenegger. "I felt like he was looking out for me, as a paternal figure would."

At 5ft 2in, the petite Clarke doesn't exactly look like an action hero. By her own admission, on Thrones, Daenerys spends a lot of time commanding others what to do, rather than getting her hands dirty. Playing Connor was different, with Clarke enduring weeks of weights and weapons training to look convincing. So did she ultimately feel like a female Arnie? "There were moments, definitely, where I was running through a tunnel firing a grenade launcher," she grins. It probably took all her restraint not to yell his 'I'll be back' catchphrase.

Doubtless squaring up to Schwarzenegger was not how Clarke imagined her career might pan out. Born in London, raised in Berkshire and educated in Oxford, she describes herself as the "classic" show-off. "I came out of my mum's stomach going 'I want to be an actor!'" Aged 3, she accompanied her mother to a production of Show Boat that her father, a theatre sound engineer, was working on, and it lit a fire inside her. "My Dad is one of the reasons why I saw that this could be something I could do," she admits.

After studying acting at London's Drama Centre, Clarke got work almost immediately in television - from a well-regarded Samaritans commercial (that saw her looking to camera as tears rolled down her face) to an episode of TV show Doctors. Then came Thrones, with Clarke replacing Tamzin Merchant, who had played Daenerys in the pilot. "Game of Thrones really launched so many of us, and for me, I've been so lucky - because I've had my own time to digest it," she says. It means still living in London, without shuttering herself away. "I've got no cause for changing who I am."

The only difficulty, so far at least, has been the inordinate amount of time she spends away from her friends and family. "There are times when you're like, 'I'd just like to sleep in my own bed and just go down the pub'." Certainly, Clarke's work ethic is second-to-none. Her punishing schedule saw her go from the months-long shoot for Genisys directly into the fifth season of Thrones then straight onto forthcoming indie movie Voices From The Stone - a 1950s Italian-set tale that she compares to Hitchcock's Rebecca. "I work hard and that's what I was taught to do," she shrugs.

When we meet, she's just got one more day to shoot on her next movie, romantic drama Me Before You, based on the book by JoJo Moyes, then it's back to the day-job in August - filming the sixth season of Thrones. Finally, she's beginning to get her head round the show's unbelievable success. "This year, really, has been the first year I've come to terms with it," she nods. "I spent a lot of time going, 'What? No! How? But! Hmm!' But I've realised if you just accept where it is, and be grateful, and then carry on as normal, then everything else falls into place without it being too weird."

Terminator Genisys opens tomorrow