In bounds Dancy in self-assured fashion, casually dressed in a white T-shirt, beige cardigan and jeans, looking every inch the school cricket captain.

It’s something of a surprise to the 34-year-old English actor that he’s here at all. He candidly admits that when he filmed Adam, in the space of just three weeks at the tail end of 2007, he had expected it to sink without trace. “My working assumption was that nobody would see the movie, because it was made on such a small budget,” he says. All this changed when the film was picked up by Fox Searchlight and won the Alfred P Sloan prize at this year’s Sundance Film Festival in Utah. More recently, it was the closing-night draw at the Edinburgh International Film Festival last month. Between the original shoot and the film’s festival plaudits, Dancy shot Confessions Of A Shopaholic, in which he plays a more conventional leading man in the shape of a dashing magazine editor, Luke Brandon, and which has grossed more than $100 million (£60.5m) at the box office. It was a role befitting Dancy’s growing reputation as a heartthrob, albeit a rather reluctant one.

So why did he accept the low-budget, low-profile role of Adam in the first place? “I knew nothing about the script at all when I read it,” he says. “I was beginning to wonder, ‘What’s going on here? There’s something I haven’t been given, or at least I hope so, because otherwise this is going to be a really annoying story.’ And lo and behold a third of the way in my character says, ‘I’ve got Asperger’s syndrome.’ What I admired so much was that the script didn’t begin with Adam being labelled instantly, which would usually be the way somebody would try to tell that story.”

The film is essentially a romantic comedy about an introspective young man who falls for his gregarious new upstairs neighbour, Beth, played by the Australian actress Rose Byrne. Their difficulties in connecting with each other are compounded by a string of unhappy relationships on Beth’s part and Asperger’s syndrome on Adam’s.

Autism spectrum disorders are thought to affect one in every 100 people in the UK. As one such disorder, Asperger’s is easier to define than it is to understand. People with the condition find it difficult to read facial expressions and body language; they struggle to pick up social cues and have trouble filtering out background noise or distractions. In particular, Asperger’s impairs the ability to understand the thoughts and emotions of others, making it hard to form relationships. To the uninitiated, someone with Asperger’s can seem rigid, indifferent, rude, selfish, thoughtless or plain childish.

In playing Adam, Dancy joins a burgeoning list of actors who have attempted to portray people living at some point on the autistic spectrum, most famously Dustin Hoffman in Rain Man, but more recently Sigourney Weaver in Snow Cake (2006) and Philip Seymour Hoffman as the voice of a middle-aged New Yorker in this year’s Mary And Max. The profile of Asperger’s syndrome – often referred to as a “hidden disability” – was famously boosted by Mark Haddon’s prize-winning 2003 novel The Curious Incident Of The Dog In The Night-Time, which was written from the point of view of a teenager with the condition.

Perhaps mindful of the Law of Extras (the cynical diktat voiced by Kate Winslet in Ricky Gervais’s television show that “you are guaranteed an Oscar if you play a mental”), Dancy insists it was the quality of writer-director Max Mayer’s script that persuaded him to take the part. “It wasn’t the opportunity to play somebody with Asperger’s that appealed to me about this script at all – it was the story and the humanity of these two people trying to make contact. I felt like the script was rich in all the different tones it contained. It walked a beautiful, delicate line between the humour, the difficulty, the romance and the naivety.”

Though there are a few straight-out laughs in Adam, including a cute reference to Forrest Gump, much of the humour is understated. Adam’s quirks – his ability to reel off facts about telescopes or the theatre, or his desire to impress Beth by cleaning her windows in a spacesuit – are funny not so much in themselves, but in what they reveal about modern manners. A pertinent reversal of convention comes when Adam, having lost his job as an engineer, is preparing for an interview. Rather than mug up on his subject, which he already knows inside out, he has to painstakingly rehearse the bits of the interview that other people manage without thinking: looking the interviewer in the eye, smiling and shaking hands at the same time, sitting still.

And for a supposed romantic comedy, the film packs some heavy punches. Adam has to adjust to the death of his father, while Beth’s relationship with her parents, an outwardly successful New York couple (superbly played by Amy Irving and Peter Gallagher) darkens as her father’s indictment for accounting fraud crowbars open various cans of worms. Nor are viewers spared the harsher aspects of a condition that inhibits the capacity to compromise or show affection. Dancy defends a scene where Adam flies into a rage because Beth has told him what seems to her to be a little white lie. “You couldn’t make this movie without presenting a side of Adam that would be genuinely difficult to live with,” he says. “Just when you think things are going nicely, there’s a softness to it, but it’s not going to suddenly get easy – it’s not going to suddenly drift away.”

What Adam is fundamentally about, of course, is the difficulty in making any relationship last. “It’s made me reflect on how it’s a miracle that we ever connect with anybody in a proper, honest way,” says Dancy, “and even when we do, even when you’re in a relationship that has lasted, it’s an ongoing challenge. That’s what got me interested in this movie in the first place, and it’s something you don’t have to know anything about Asperger’s to understand.”

Dancy admits that playing Adam presented an unusual challenge, in that he was denied most of the standard tools of his craft. “Normally you rely as an actor on empathy, communication, openness; actually, Adam has openness aplenty, but those other things I was stripped of.”

Dancy has shared a screen with a sparkling constellation of leading ladies: Keira Knightley (whom he has called “a lot of fun”) in the forgettable historical romp King Arthur; Anne Hathaway (in Ella Enchanted); and Emily Blunt (in The Jane Austen Book Club). He met his fiancée, the American actor Claire Danes, on the set of Evening, a pensive romantic drama that had a difficult critical ride. When it comes to his Adam co-star Byrne, though, he gives me a guarded smile that suggests he thinks I’m looking to him to confirm some piece of on-set gossip (in fact, I’m not – you could call it an accidental bluff). In any case, Dancy decides to get his retaliation in first. “It was great working with Rose,” he says. “I loved the whole experience, but I didn’t get a strong sense of Rose. We didn’t have the normal interactive experience actors usually get. I think it’s pretty obvious that I was working kind of in a bubble because of the character I was playing. She may have just thought I was a really uncommunicative, difficult bastard, but I think it worked out well for both of us and for the film.” So how did Byrne compare with his other screen partners? “I think comparisons might be a little pernicious,” he replies, laughing.

When it comes to talking about his own relationships, Dancy is known for his reticence. He started dating Danes in 2007, shortly after he ended a 10-year relationship with the artist Annie Morris, who illustrated Sophie Dahl’s children’s book The Man With The Dancing Eyes. While Dancy was promoting Confessions in February, news emerged that the pair were planning to marry (in France, in September, according to subsequent rumours). “There’s no news on that front,” says Dancy, his jaws clenching. On the question of how the couple deals with being paparazzi fodder, though, he is more talkative. “You deal with it by not engaging with it too much as a topic,” he says. “Not letting it become a factor in your relationship and not throwing yourself into scenarios where you’re going to attract that kind of attention.”

Though Dancy has been acting since he left Oxford with an English degree in 1997, he is still seen as a rising star. Much of his early career was spent making period dramas for television such as Daniel Deronda and Elizabeth, with Helen Mirren (acting with the grand dame, he says, was a “remarkable experience”). Since breaking into Hollywood with King Arthur and the Rwandan-based drama Shooting Dogs, he has carefully balanced classic romantic lead roles, such as Confessions, with more idiosyncratic parts, including nerdy Griggs in The Jane Austen Book Club, and, of course, Adam. He is less adverse than he once was to the heartthrob tag. “I’d rather be labelled heartthrob than … Well, there are a lot of other things that are far worse. But by and large that’s only ever something you encounter when you’re talking to the press. It’s certainly not important to me.”

Ultimately, Dancy says his choice of roles comes down to instinct. “You have to be

careful because you’re not your own master as an actor,” he says. “You can set ground rules, like, I want to find a bigger movie now I’ve done three of these little shot-in-the-dark kind of films,

but then another one comes along and you love it. I never try to micro-manage my

career beyond attempting to persuade the people who send me scripts to send as many as they have, and remaining open to what’s good.”

Gut instinct. That might be a foreign concept to Adam, but so far it has served Hugh Dancy well.

Adam (12A) is released on August 7