Rising Scots actor Chloe Pirrie on BBC spy drama The Game

The bleak, tender portrait of love, loss and loneliness shot in the Highlands premiered at the 2013 Glasgow Film Festival. Watching Pirrie in the title role, it was impossible not to imagine the young Edinburgh lass as a star of the future. A richly deserved Independent Film Festival award followed, and it seemed a question of when, not if she would make the break from small, micro-budget independent film to the big league.

A key role in The Game, a major new espionage thriller set during the Cold War, which begins on BBC Two this month having already aired to acclaim in the US, suggests Pirrie is indeed embarking on that journey, with further exciting roles lined up for 2015.

The 27-year-old stars alongside Brian Cox, Judy Parfitt, Tom Hughes and Shaun Dooley. And, in news that will surprise nobody who saw her film debut, Pirrie is terrific. Shot in late 2013, this tale of MI5 operatives attempting to stay one step ahead of their KGB counterparts takes its stylistic cues from the recent adaptation of the classic Tinker Tailor Soldier Spy and oozes class.

Pirrie plays Wendy Straw - "we called her Bendy Straw on set," she laughs - who begins the series as wide-eyed, out-of-her-depth secretary, becomes PA to Daddy (as Cox's head of MI5 is known) and an integral part of the team, acquiring dangerous levels of classified information along the way.

"She is quietly very ambitious," says Pirrie, to whom the same description could perhaps be applied. "She has to juggle being subordinate but also having to run their life for them and sort everything out. She is all about her work; she'll be Stella Rimington [former head of MI5] in 15 or 20 years time."

We are meeting in London, where Pirrie has lived since graduating from the Guildhall theatre school in 2009, though the tartan skirt she wears to our interview on the fifth floor of Shoreditch House suggests she retains a strong sense of home.

Pirrie was bitten by the acting bug while attending the independent, all-girls' Mary Erskine School in Edinburgh. She recalls with a smile the way she was inspired by drama teacher Dr Scott ("I need to write to him. I think he is still there"), who cast her in a production of The Cherry Orchard. "Chekhov. Quite an ambitious thing for a bunch of teenagers to tackle. I was Anja and absolutely loved it. I felt like I had been set free," says Pirrie.

On one of many trips to the theatre in her late teens, the idea of acting as a career was cemented in her mind. Despite achieving good grades, especially in English and history, university was no longer an option. "It was quite an unconventional path to be going down at my school, but I wanted to do the things I was writing about rather than theorise about them. I wanted to tell the stories, rather than talk about them. I was falling in love with theatre and acting as a way of making sense of the world.

"I went to anything that was on at the Lyceum in Edinburgh. I was quite geeky. There was a production of Look Back in Anger with David Tennant and Kelly Reilly in it, and it blew me away. I still think about it and look back on it as the moment where I decided: 'I want to do that.'

"Both of them were extraordinary, and this was before David Tennant was famous. He was still a jobbing actor. But he was extraordinary. I went as part of a school trip and there were all these other kids around me. Most of them enjoyed it, but it was a typical school party, quite noisy. I sat there mesmerised.

"If you are ever on stage and it feels as though the audience is not laughing at the right points, or are not quite as engaged as you'd hope, you have to remember there is always somebody who might be falling in love with this world and having an epiphany. I was that person."

Pirrie's enthusiasm is infectious. The world of internationally renowned co-stars in high-class dramas (more of which later), attending awards ceremonies and appearing on the front cover of this magazine ("Am I going to be on the cover? Oh god!") is new and full of wonder for a young actor who worked in a series of Edinburgh cafes before getting into Guildhall at the second attempt, and has worked in a series of London bars since graduating. "It was daunting, moving to London on my own. But my mum is originally from Epping and I'd spent a lot of time with her showing me around where she lived and worked, so I felt comfortable here," she says.

"In a lot of ways it felt like going home. I had a very strong sense that this was my life. I wanted to leave Edinburgh quite strongly at the time, no offence to Edinburgh. It was the place I had grown up and I felt quite constricted. I wanted to be free and away and on my own.

"I felt such a sense of achievement having got here. I had proved I could do it. But it is daunting. London can be quite lonely and a hard place to live, but I do love it. It is where I forged my way to live. It is where I call home."

It is also home to the vast majority of established and aspiring actors. The acting community may be strong, but the competition is fierce. "You feel like one of a million people trying to do this," she admits. "My early years as an actor felt like going back to trying to get into drama school. You have cracked one level, now you are starting again. So it is exhausting, and hard to keep up your enthusiasm and passion for it.

"There have certainly been hard times, lean times, but I was so young. It was great to meet people who weren't involved in the world I was in; you have to feed yourself with exciting things that are not just acting, acting, acting. It was healthy to develop a life outside my ambition. And then Shell happened."

Solstice, a short film in which she appeared, had been seen widely within the industry, including, most significantly, by writer-director Scott Graham, who was trying to get the money together to make his debut feature film. After a year of meetings, auditions, rejections and setbacks, Pirrie was finally cast alongside Joseph Mawle. During this process, Pirrie had made her debut at the National Theatre, in Men Should Weep by Glasgow's Ena Lamont Stewart. "It was a wonderful cast. All these brilliant Scottish actors. Suddenly I had all these Scottish friends in London," recalls Pirrie, who appeared alongside Sharon Small, Robert Cavanah and Morven Christie.

And Shell itself? "I kept working in bars, went on holiday - I didn't believe it was going to happen until I was up in the Highlands and taken to the set to start filming," she says. "Independent film, I now know, is like that. Nobody has the money or the time. It makes me think it is a miracle that anything gets made, let alone something successful that wins awards. It was a very lucky break."

The film is a revelation. "I felt a strong connection to the script," says Pirrie, whose character lives at an isolated petrol station with her grieving, widowed father. "Joseph Mawle and I lived together in a cottage for a couple of weeks before we started filming, trying to get to know each other. We were able to really immerse ourselves into it.

"It was a very intense shoot, but because it was my first big thing, I was so full of excitement and this vigorous work ethic. I was determined to make the most of it and not let the opportunity go to waste. I threw myself into it, which you have to do in certain types of role. She is in pretty much every scene. I knew it would be hard work, but I knew I had so much I wanted to give in it.

"It is weird to watch it. I loved it, but at the same time, you are confronted with your face from close range and the camera doesn't miss anything. You feel very exposed."

The effect of starring in a small but critically acclaimed film is not sudden fame and fortune. "Nothing changes overnight unless you win an Oscar," says Pirrie. "You move up a little bit, but you are always a little fish - just in a slightly bigger pond."

Pirrie threw herself into the sink or swim world of auditions, albeit for bigger and better roles. A part in Black Mirror, Charlie Brooker's anthology of bleak one-off films, showed her range.

"It is lovely to be going up for so many roles, but the volume of responses is relentless. I was rejected for a few things as well," she says, showing an unusual degree of honesty. "I had a week where I was turned down for three really great projects. Sometimes I am good at dealing with it - 'That's fine. Next' - but once a character gets into you and you start to care about them, you want to tell the story of who they are: 'Damn it, just cast me!'"

Now Pirrie is making waves. Sky Atlantic's hotly-anticipated heist drama The Last Panthers starring Samantha Morton ("I was watching her the other night in Morvern Callar - I love that picture, she is extraordinary") is already in the can, as are indie road movie Burn, Burn, Burn (with Downton Abbey's Laura Carmichael) and Paolo Sorrentino's film Youth, which premieres at Cannes. Pirrie is on a hot streak.

After we meet she will go to Lithuania to film the BBC's big-budget adaptation of War and Peace, playing Julie Karagina alongside the likes of Gillian Anderson, Paul Dano, Jim Broadbent and James Norton, having just finished An Inspector Calls with David Thewlis and Miranda Richardson for the BBC's upcoming literary classics season.

"I'm thrilled to be part of these fantastic projects," says Pirrie. "It's a joy to be working in such different periods with such contrasting characters and with such exciting casts."

First, though, there's The Game. "It is classic espionage," she says. "The Cold War is in full swing, so it is a very scary time. The 1970s are in colour, which makes it seem so much more recent. But the technology is nowhere remotely near. It is interesting to consider their jobs, as spooks, without any mobile phones. The gravity of the situation hits you. You can't text them to call the mission off ... or warn them that the bomb is coming."

We got advance notice of her talent with Shell. Now Chloe Pirrie is on her way to claim a place at the top table of British TV. Consider yourself warned.

The Game starts on BBC Two, April 30, 9pm.