'Yeah," laughs Rebecca Hall. "Just like me."
She's huddled up in a soft leather couch in the Merrion Hotel, hugging her legs, her long black hair falling down over a flimsy unbuttoned dark blue shirt. We're talking about how a one-square-mile neighbourhood of Boston called Charlestown has produced more bank robberies than anywhere in the US. Crime has become like a family business fathers pass down to their sons.

Not that she's a criminal, although she unthinkingly falls in love with one in Ben Affleck's terrific thriller The Town, which focuses on the operations of a masked Charlestown gang that sticks up her bank and takes her hostage: later she meets the gang leader, played by Affleck, in a launderette without realising who he is.

Her family business is not crime but acting. Her father is the English theatre and film director Sir Peter Hall, who founded the Royal Shakespeare Company and for many years ran the National Theatre. Her mother – his third wife, his first was Leslie Caron – is the fiery American soprano and mezzo soprano Maria Ewing, who famously appeared nude in Hall's acclaimed 1992 production of Richard Strauss's Salomé at the Royal Opera House. "It was only a few seconds," Ewing said of her provocative dance of the seven veils, "they had to listen to me singing for nearly two hours."

So, having grown up in rehearsal rooms as Hall mostly did, acting is surely in her blood? "You mean I couldn't do anything else?" she teases. Well, perhaps she might have been an opera singer: has she a voice? "I do, but someone would have to pay me an awful lot of money to do it in public. It's very tough." She points to her throat. "You have to rely on that muscle, which can go wrong. Terrifying, very very terrifying."

It was always more likely that acting would seduce her. She grew up with her father after her parents divorced when she was five. They had been married eight years. "I went a lot to America on school holidays and visiting – my mother is from Michigan and worked a lot in New York – but I never lived there and I never went to school there, or picked up an accent. But I definitely was more saturated in American culture than most children of my age growing up in England."

She feels English or American depending on where she is. "I have a foot in both countries. But if I'm being completely frank, I feel more English. I grew up in London. All my friends and family are in London. I've got a London accent. Everything I know is London. But I suppose I feel that in New York as well. If I'm forced to identify myself as one or the other I'm definitely English, but maybe I'm a bit of nowhere land."

Which perhaps is the essence of being an actor: their job is to keep being different people in different worlds. She grew up accustomed to blending in wherever she was, surrounded by people to whom performance was a way of life. "It was a great upbringing. I couldn't have asked for a more diverse and eye-opening childhood. But that's not the same thing as saying I didn't have a choice, because I definitely did. I wasn't bullied or prodded into acting by either of my parents. They would support me to do what I wanted to do. But it's what I like and what I love so why wouldn't I do it?"

When she was eight her father cast her as young Sophy, all dressed up in a girlish frock and ankle socks, in The Camomile Lawn, a Channel 4 mini-series version of Mary Wesley's novel. "I took it very seriously. I was sure acting was what I should be doing. But I wasn't boisterous about it. I was quite a shy child. I think I always have been introverted. But when it comes to acting I can't remember a time of not knowing what I wanted to do and having a quiet determination about it."

Shyness seems to go with acting: it's as if it is only by becoming someone else actors can be themselves. Her friend Sinead Cusack, with whom she toured the world in Sam Mendes's production of A Winter's Tale before filming The Town, says acting is the shy person's revenge on life.

"If you're afflicted by shyness it can hit you at the strangest times," Hall says. "I can be incredibly confident and nobody can shut me up some days, and other days I find it difficult to have a conversation in a shop with somebody about change. I can feel myself retreating and wanting to disappear. It hits you out of the blue if you have it, and I definitely do."

The advantage if you're an actor is that it makes you more observant. "People who by nature are introverted tend to spend a lot of their life watching other people and thinking about their behaviour and listening to how they talk. I love doing accents. Even if I play someone from London, I make the voice specific to the character because everyone has their own accent, certain ways of talking that make them unique and are a huge part of their personality, and that fascinates me. Everything you do in life enriches the skill of acting. I love doing jobs when I don't at all relate to the characters and I know nothing about where they come from or why they do what they do. Acting is all about curiosity"

Unusually for an English actress, Hall has no formal training, but then her whole upbringing indirectly taught her more than anything she could pick up at Rada. It has also meant that she sounds real in a role, rather than giving an actressy performance. "Your early experiences make you who you are. You have an understanding about the profession more than you do any other one. You develop a passion from that experience. It seems a natural thing to do."

At 20, she dropped out of Cambridge where she was studying English literature to play Vivie in her father's production of Mrs Warren's Profession – winning the Ian Charleson award – and then became his Rosalind in As You Like It, before making her screen debut as Rebecca Epstein in Starter For Ten. "Two weeks after that I went to Los Angeles and started The Prestige with Christopher Nolan. I'm lucky that I went straight into working with incredibly established directors."

Such as being cast by Woody Allen in Vicky Cristina Barcelona – his most successful film for years – and in between playing a Tony Blair aide in Ron Howard's Frost/Nixon, appearing with Michael Gambon in Stephen Poliakoff's Joe's Palace and winning a Bafta for the Channel 4 serial killer series Red Riding.

"I don't know why Woody cast me in Vicky Cristina Barcelona," she says. "I'm so thankful he did but it was bizarre. It literally just dropped in my lap. I didn't audition for him. I'd done nothing that had come out. He'd seen nothing that I'd done. He trusted his casting director Juliet Taylor, who had seen me in As You Like It. And then I just met him and he said to me, 'Can you do an American accent?' I said, 'Yes', and he said 'Goodbye', and that was it. Two weeks later I sat there reading the script and by page 16 I was practically in tears going, 'I can't believe this is happening, someone made a mistake', it was so extraordinarily out-of-the-blue to get a part like that."

Her performance as an about-to-be-married American girl on holiday in Spain with her friend Scarlett Johanssen, swept off to Oviedo for a weekend by Javier Bardem, who makes no secret of his intent to bed one or both of them although he's still in a tempestuous relationship with Penelope Cruz, caught the eye of Ben Affleck and led to her being cast in The Town.

"I'd seen her Vicky and in The Prestige and talked to Chris Nolan," Ben Affleck tells me later. He loved her. "In Vicky she just showed such a range and grace and yet she was still real. She was accessible. You need to fall in love with her, otherwise The Town won't work. But you don't fall in love with her the way you would with an artificial Hollywood glammed-up star who's kind of unattainable and superficial. Rebecca is graceful, lovely and elegant but also seems like a person who if you're lucky you might meet."

Just as his character does at a launderette while she's running her clothes through a washing machine: the realness of their relationship involves the audience in the action and makes even the spectacular car chases and shoot-outs grippingly believable.

"She knows how to be that outsider so well," says Affleck. "As the audience, we can see her as this normal person stepping into his world rather than just being immersed in it and letting it become our reality. Her presence reminds us always how unreal it is."

Affleck, whose debut film Gone Baby Gone suggested directing might be his real talent, shot far more takes than he could use in order to provide Hall and the other actors with a creative environment in which they could have room to experiment.

"All the time we took was to massage the performances to a place where she felt she had turned in her best work. I just turned the camera on. We shot a lot of footage. I knew I could do the directing in the editing room because everything she would do would be real and interesting. And then it just became a question of choices – do we want to have her a little more hurt or a little more flirtatious or a little more guarded."

The Town's opening weekend gross of $27m put it top of the US box-office charts, guaranteeing that Affleck will have the clout to consolidate his growing reputation as a director. It should also propel Hall into the Hollywood A-List.

She'll next be seen with Will Ferrell in Everything Must Go, which is based on a Raymond Carver short story. "It's really intriguing. Will plays an alcoholic, which is quite a departure for him. It's not like his other films. His wife throws him out with all his possessions on the lawn. He's five days to sell them and pay his bills. I'm a neighbour who helps him out."

During the summer she filmed a small English supernatural thriller The Awakening, set a few years after the end of World War I. Her character is an eccentric rationalist out to prove that ghosts don't exist. It's the first film in which she's in every scene, every frame, and every shot.

In November she starts rehearsals to play Viola in Twelfth Night, a production her father is directing at the National Theatre. "The rehearsals will coincide with his 80th birthday," she says. "Twelfth Night is one of his favourites. He's directed it three times. The last time we worked together was in As You Like It nearly seven years ago. He has always said we have to do Twelfth Night one day. I've always said, yes, absolutely. So now it's happening. I love working with him."

Strangely, it will be her first appearance at the National. "I spent much of my childhood there. I probably learned to walk in the wings as a toddler when he was running the building. I'd run around back-stage. I remember the smell of it so much. When I'm there I have a strange feeling I haven't had since my childhood. It's peculiar and quite moving for me actually finally to be working there."

'The Town' is on general release