Ruth Negga looks over her shoulder. "Hold on a minute," she says, leaning back to peer beneath our cafeteria table on an upper floor of the RIBA building in central London. She bends to look under her chair. "Where is my movie career?"

The 30-year-old actor is clowning, and this is her way of telling me I've touched on a subject that has come up before. A best newcomer nominee at the Olivier Awards back in 2003, Negga has had memorable success in the theatre across the intervening decade, particularly at the National: Aricia next to Helen Mirren's Phèdre, Ophelia opposite Rory Kinnear's Hamlet. And she's done plenty of good telly too: she was Shirley Bassey in the well-liked BBC biopic Shirley last year, and is soon to appear in Channel 4's impressive political drama Secret State.

But movie work? Patchier. There was a role written for her in Neil Jordan's 2005 drama Breakfast On Pluto. She was the dame in an unremarkable Samuel L Jackson action flick, The Samaritan, released in April, and she'll be in Steve McQueen's new film next year. It's unfathomable to me that she isn't used more.

Negga's a powerful actor, the voice low and layered with bite. Her expression, in neutral, has a sort of stoic hurt to it, making her an ideal tragedian. And it can't go unmentioned that she's stunning to look at: half Irish, half Ethiopian, massive eyes, pronounced chin and cheekbones. Yo, Mendes, Nolan, Boyle: get in touch.

"I'm not in any rush to get anywhere," she says. "There's a pressure on actors to get somewhere before it's over. But everyone wants longevity, don't they? It's a career. Why be that flash-in-the-pan, taking every job out of worry it'll soon be over?"

Negga was seven when her Ethiopian father died in a car accident. She was raised by her Irish mother, a nurse, and they moved around before settling in Dublin, where Negga went on to study drama at Trinity College. She once credited her itinerant upbringing for an ability to pick up accents: Shirley Bassey's distinctive Tiger Bay, for instance. In Secret State she plays a meddlesome MI6 agent called Agnes, a character loosely based on real life spy-turned-whistleblower Katharine Gunn and for which Negga adopts crisp RP. In the McQueen film, Twelve Years a Slave, she'll be a slave from the deep south.

Negga has needed to make herself a chameleon. In September she told an Irish tabloid that Hollywood casting agents have sometimes been baffled by her: mixed-race, Ethiopian-born, Irish-accented, London-based. It sounds an unimaginative bias, if true; perhaps she inspires hesitation in other ways. Only 5ft 2in (and wrapped today in a woollen scarf long enough to mummify her entirely), Negga is small, bird-like, but patently relishes a scrap. Sorry Shakespeare: "Ophelia is underwritten, a really strange part." And deciding whether to take a new acting job, a possible fork in the career, is "like a Robert Frost poem, every time". Overall you get the sense that Negga isn't a put-me-where-you-want-me actor.

"When you work with directors who really love actors, who love their contribution, it feels amazing. But sometimes when you work with directors you feel like you're in the way. A pawn that they have to manipulate to get their point or their art across." Steve McQueen was one of the goodies. "There's absolutely no bullshit about that man whatsoever." Indeed, Negga liked McQueen so much, "I went into a swamp for him."

It was a runaway scene, her character, an escaped slave, making away through "a real Louisiana swamp. Sewage in there, and alligators. Water moccasins, all kinds of things. The stuntman told me not to worry, it was only knee deep. Knee deep for him!" She gestures to where the sewage-water actually reached. Armpit height.

Getting filthy was a feature of her work in Phèdre, a hit for the National back in 2009. I have an abiding memory of her taking her bows, absolutely plastered in stage blood. She had it splashed all over her face, neck and torso, Negga's character, Aricia, having clung to and kissed the dead body of her lover Hippolyte, played by Dominic Cooper. "A critic wrote that it was too much blood. It probably was," she says. Nonetheless, she was backstage every night coercing the make-up team: "More!" Director Nicholas Hytner eventually had to intervene and tell everyone to tone it down. "But I thought, God, it's the fucking Greeks. Of course she kissed his tattered, trampled body. It's love! You don't come to see a Greek play and not want blood and gore and depth of feeling from your boots up."

Gossip at the time had Negga in an off-stage relationship with Cooper. She denied it in a 2010 interview ("Absolutely ridiculous"). Then in July there were long-lens photographs taken of the pair, smooching on an Italian beach. "If people want to invade your privacy they want to invade your privacy," she says, of the paparazzi. "I find it chilling and I find it awful and it makes me really nervous. It hasn't happened to me much but when you have a taste of it, it's bitter."

More Hollywood work, I say, would probably up the likelihood of intrusion. She nods – although, "some people can manage being a household name, get access to really good parts, and no one [from the gossip press] has any interest in them. I don't know how that works."

The ultimate benefit of being an actor, she thinks, is "not having to take the same route to work every day". The stuff around the edges – "uncertainty and insecurity"; reading comments about yourself on the internet; paps on the fringes of your summer holiday – that's a kind of reluctant payment for having a job that satisfies.

"I didn't become an actor to make money. And I didn't become an actor to be famous – though people always gasp when you say that, as if it's unfathomable that an actor doesn't want to be a star. I like connecting with people, and that's what good art is, a point of connection. There's nothing better, on stage or on film, than feeling like you've achieved that."

Secret State starts on Channel 4 on Wednesday