Aaron Johnson and Ann-Marie Duff in Nowhere Boy

It's early afternoon and 19-year-old Aaron Johnson is struggling to stay awake. No need to ask why. The night before, he was at the unveiling of Damian Hirst's latest paintings of blood-spattered crows at BritArt guru Jay Jopling's ultra-trendy White Cube galleries in Mayfair and Shoreditch. Tabloid pictures show him holding hands with Jopling's one-time protégé and former wife, Sam Taylor-Wood. The couple fell in love earlier while Taylor-Wood filmed him portraying John Lennon as an adolescent in her debut feature Nowhere Boy. "We're very happy together, and are hoping to get married in August," said the 43-year-old director, mother of two daughters, announcing their engagement two months ago. "I never expected anything like this to happen."


So here's the tee-shirted teenager flopped out on a couch in London's Soho Hotel, yawning. He doesn't seem particularly fazed by his sudden celebrity status. "It's nerve-wracking, overwhelming," he concedes. "But it's all part of the job." He's hoping to do another film with Taylor-Wood. "We've a great understanding, so to work together is great. But for now we're just taking time out to think."


He empathises easily with the emotional conflict experienced by the schoolboy Lennon caught in a tug of war for affection between his stern aunt Mimi, who reared him, and his free-spirited mother Julia who, he belatedly discovers, lived around the corner all his life. "He was trying to find himself and to find love, and he found it through the music his mother brought to him. She was a bit before her time"


Taylor-Wood auditioned Johnson last Christmas. "I knew when he walked in the door it was going to be him," she says. "He had a look that I knew was going to work."


"Yeah," he says. "She saw me, but she saw a ton of others too. I guess she had to convince the producers to go for me and not a name. It helped that I was filming Kick Ass with Nicolas Cage at the time. So they agreed. After that we just bonded."


Nowhere Boy is John Lennon before the Beatles. The group isn't even mentioned. "It's just a great family drama," says Anne-Marie Duff, who beautifully captures the vitality and rebelliousness of Lennon's mother. "It doesn't matter who he is or what he ended up being. Julia's always been something of an enigma because she died so young. She's so charming for him. So we see her through an adolescent's eyes. It wasn't that tricky playing mother with Aaron. He's very emotionally available. He has that loving quality where he's just beginning – it's just starting for him. It's very infectious acting with someone like that. It reminds you of why you're an actor."


The Beatles were long before Johnson's time. "I grew up in the 1990s which was a pretty shit era for music," he recalls. "Music stopped at punk. I'm not a musician but it was fun learning to play guitar. It's kind of stuck with me now. I've discovered Mozart. I've a box set and we're playing his Requiem at home."


He started acting at six on the West End in An Inspector Calls. "I played a ghost. I'd get home to bed in High Wycombe after midnight, be up next morning for school and then back into London again." He was the young Edward Norton in The Illusionist and had parts in Shanghai Nights and The Thief Lord before catching the eye in Gurinder Chadha's coming-of-age comedy Angus, Thongs and Perfect Snogging.


Taylor-Wood sees parallels between Lennon's childhood and her own. She too was left first by her father and then, when she was 15, by her mother, only later to discover that she was living down the street. "I became an artist by chance. I kept trying not to be one, but I have this feverish imagination." Her photographic installations were nominated for a Turner prize. If she wasn't photographing herself – most recently in a series of floating self-portraits in which she hangs from a roof, suspended by wires that are digitally removed – she was capturing the famous in off-guard moments. She filmed David Beckham sleeping and Robert Downey Jr crying. So she's hardly bothered by publicity over her engagement to Johnson.


Duff is different. She's the daughter of Irish immigrants who met in London's Shepherd's Bush in the 1960s. She grew up on a council estate in a home full of music. "No need to ask who Philomena Begley was there," she laughs. "I was a Beatles fan in my teens, but less of a John Lennon fan. I didn't have that precious sense of him. So I could be objective about him in Nowhere Boy, which is good for storytelling.


Her father persuaded her to go to drama school. "I started doing youth theatre as a child not because I had any grand aspirations but just because a friend did."


She made her breakthrough as the big-hearted sister Fiona in Shameless, Paul Abbott's irreverent family drama set on a Manchester council estate. She's now married to James McAvoy, who played her car-thief boyfriend Steve on the show. Unlike Taylor-Wood, she prefers to keep her personal life to herself.


Ask if she'll work with McAvoy again and she just smiles. "I only speak for myself," she says. "You'll have to talk to him about that. I act with people I want to act with. I just do what turns me on. That's all I'm saying."


She's just played the ballerina Margot Fonteyn in BBC4's Women We Loved series, managing to be utterly believable as an icon who in her 40s tries to look younger for her dazzling Russian lover Rudolf Nureyev. She's also been Elizabeth I in The Virgin Queen and Cordelia in King Lear.


Her film breakthrough was in 2001's The Magdalene Sisters, playing a country girl raped by a cousin and promptly dispatched to the nuns because she shamed her family. The Vatican denounced its director Peter Mullan – who shot the film near his home in Scotland because obstacles prevented it being filmed in Ireland – as a hypocrite, and his revelation of abuses inflicted by nuns on so-called "fallen women" at the Magdalene laundries in Ireland as an "angry and rancorous provocation".


"It was a real tipping point," says Duff. "Suddenly, like dominoes, all over the world, not just in Ireland, there were dreadful stories of clerical abuse. And it still goes on."


'Nowhere Boy' opens on 26 December