As a child Agyness Deyn had a rather unusual aspiration.

"I told my mum I wanted to be a bed tester," begins the 29-year-old model-turned-actor, "someone who could try beds and tell people which are the best." Maybe she was a born dreamer, I say. "Maybe, although it was probably more the fact I just used to love sleeping. Mum would have to drag me out of bed to get me to school."

If Deyn's ambitions have changed, whisking her from comfy bed to glitzy catwalk and now to silver screen, those early yearnings have left their mark; in person she is softly spoken and somewhat dreamy, far removed from the super-hip party girl so often portrayed in the tabloids.

We first meet on the set of her debut major film, the indie gangster flick Pusher, which opens next week. She is a single girl at the time – her romance with American actor Giovanni Ribisi, which led to their wedding this June, is still on the horizon.

Deyn looks fantastic but in a very girl-next-door kind of way, and seems far removed from the stylised model whose face has appeared on myriad magazine covers, pocketing a tidy bundle in the process. Her clients include Armani, Mulberry, Burberry and Vivienne Westwood. She even replaced Angelina Jolie as the face of Japanese cosmetics firm Shiseido.

"But then I stopped enjoying modelling," she says when we turn to her move into acting. "I wasn't looking to desperately become an actress. It is just that I got to a point where I didn't do much modelling for a while. I wanted a break from it."

Deyn had worked as a model for almost a decade and says she began to feel as though she was "on autopilot". She took a year off and relaxed in the US. "It was very full-on and very fast when things took off with the modelling," she says. "It was then that I decided I wanted to try acting, to do something for myself."

With fresh ambitions in sight, Deyn, who was born Laura Hollins, dipped her toe in the water with a tiny turn as Aphrodite in the 2010 Hollywood blockbuster Clash Of The Titans and roles in a number of short films. Earlier this year, meanwhile, once she had finished Pusher, she took on her first stage role in The Leisure Society, playing Paula, a flirty dreamer who's invited to a dinner party. She earned strong notices for her role in the play, which ran at Trafalgar Studios in London's West End.

"I wasn't terrified, funnily enough," she says of the experience. "I felt safe with Paula and I never knew how I would feel because I had never done it before. What was interesting was that the space was so small." Trafalgar Studios holds around 100 people, with the stage open on three sides, "so it is kind of in the round and the audience are literally right there sitting next to you".

That did cause the occasional faux pas, she recalls. "One night I leant back in the chair – which I sometimes do – and I ended up putting my head on someone in the audience's knee. Obviously you can't do that and you are just like, 'F***.'"

It was the early word on her performance in Pusher that helped secure Deyn the leading role in The Leisure Society, and with her career now snowballing it was her turn in that play which earned her a career-making shot at the big time, playing Chris Guthrie in a film adaptation of Lewis Grassic Gibbon's masterful novel Sunset Song. "I would love to do something a bit more edgy," she says when we're on the set of Pusher, "something where the characters are really complex." Published in 1932, Sunset Song clearly fits the bill. The first instalment in Grassic Gibbon's A Scots Quair trilogy, Sunset Song is widely regarded as among the most influential Scottish novels of the past 100 years.

Directed by celebrated British filmmaker Terence Davies, who made last year's critical hit The Deep Blue Sea, the adaptation will also feature Peter Mullan. Set in the early 20th century in a poor rural community in the north-east, the story recounts Chris's struggle to keep her family afloat amid the growing pressure of industrialisation and the encroaching shadow of the First World War. "The script is amazing," says Deyn, "and you can't help but totally fall in love with the story and the character of Chris Guthrie. I can't wait to get started and just hope I can do justice to the character."

Whether Deyn has the skill to bring such a complex character to life remains to be seen but she's earning plenty of plaudits for Pusher, an English-language remake of the 1996 Danish original. Deyn stars as Flo, the love interest of Pusher's central character, a small-time drug dealer called Frank, who is played by Richard Coyle. Though she is a supporting player, the film is at its best when Deyn is on screen.

Indeed, Deyn's character is expanded from Nicolas Winding Refn's original film and the Spanish director of the remake, Luis Prieto, says he was initially reluctant to cast a model with precious little acting experience in the role of Flo. He found himself with no other choice, however.

"They said one of the auditions would be from a supermodel but I wasn't really interested in someone with no real acting experience," the filmmaker explains, "so I simply said I would watch all the auditions and choose my favourite actress. As you can probably guess, the one I chose, without knowing she was the supermodel, was Agyness, and it was the right choice; she was just wonderful."

On the set of Pusher, sitting on a church doorstep in Hackney, east London, Deyn says, "Flo is a heroin addict, she's a dancer, and she is caught up in this grimy world. She is working to use and using to work so there is this chain where she is caught but she has the dream that it is just temporary. She is fighting all the time."

The route to her freedom, she hopes, is Coyle's character, Frank. "Flo is so in love with him but she can't seem to penetrate him, psychologically or emotionally. She is a bit of a train wreck herself and she is looking for that serenity that she thinks she's going to get from this perfect relationship, this perfect life."

If things are going swimmingly for Deyn at the moment, they all started very humbly. When she was growing up in Lancashire she was an average schoolgirl with a love of films like The Goonies and Dirty Dancing, "which I used to watch over and over again". She also held down a part-time job in a fish and chip shop. "She was a normal, lovely girl who would serve the chips, wash up or do anything you asked," the chip shop owner said, once Deyn had hit the headlines, "but she had charisma and I knew she would do well. She always got a great reception from the customers."

After leaving school (and the chippie), Deyn was spotted by a model scout in London. She quickly embraced the lifestyle, becoming the "it girl", mingling at all the parties and immediately identifiable – for a while at least – thanks to her trademark cropped hair. Dressing outrageously, she says, was always appealing. "When I was young I dyed my hair bright pink then shaved it off and my mum was like, 'What have you done?'" She giggles. "My sister was the same. She had bright dreadlocks."

Her mother would buy her daughters matching dresses from Laura Ashley, "but then my sister would go out to family dos with piercings and tattoos and I'd have a shaved head", she laughs. "It was so funny. We both wear quite girly stuff these days."

The second time we meet, in a swanky London hotel, she is draped in a flowery dress and a pair of Adidas trainers. Her hair is bob-length. "I feel that my wardrobe has simplified a lot," she says.

"From my teenage years through to my late 20s my style was full-on, with lots of experimenting and crazy punk outfits, but then I kind of felt I wanted to be a bit simpler."

Her life in general, she says, has become simpler, especially since she moved to Los Angeles. The partying that accompanied her years on the catwalk has given way to a settled relationship with 37-year-old Ribisi, an American character actor known for his intense and often screwy on-screen portrayals in TV series My Name Is Earl along with recent movies The Rum Diary, Contraband and Ted.

Ribisi, a Scientologist, allegedly walked out on his girlfriend, singer Chan Marshall (aka Cat Power), just two months before wedding Deyn in June. The couple are now settled on the west coast.

"I am happy living in LA," she says. "I have a lot of friends and I wanted to feed into that lifestyle a bit more, to be outdoors with the sun and to be healthy.

"You can hike up a massive hill in LA and you can see the sea from the top. There's Hollywood, and you can drive to the beach. I love it."

The couple are being stalked by the paparazzi, however. Deyn appeared in September's gossip pages smooching with her new hubby in the supermarket, a jar of nutty sandwich spread in hand, and this week was forced to deny rumours that she would become a Scientologist.

Throughout her rise through the realm of fashion and then into filmmaking, Deyn has consistently received the backing of her family.

"They were very supportive," she says. "At first I worked hard for a lot of years before I got success financially, grafting for years, going to Paris, to Milan, doing the whole circuit and mum would send me money. She has always been there for me."

These days, of course, Deyn no longer needs her mum to drag her out of her bed, and if she does still, on occasion, harbour dreams of testing beds, she could easily be forgiven — she is a newlywed, after all. n

Pusher (18) is released on October 12.