Somewhere in the hills above the Sunset Strip, under a sky of pure Californian blue, Matthew Rhys is contemplating the many difficulties of being a Welshman in LA.

“Here's the thing with Americans, right,” he says, in an accent as thick as the air in a Cardiff chippie. “They go out on a Friday night, and they go, ‘Oh, I'll get a little bit buzzed.' One of my mates came over a few weeks ago and he said to me, ‘What do they mean, buzzed? Are they takin' drugs?' I said, ‘No, it means they're having two drinks and getting a little bit tipsy.' To which he replied, ‘Why would they do that? Why wouldn't they just get smashed?' And that's the thing, isn't it? On a Friday night, I like to get smashed. At home, everyone else is smashed, so it's completely normal. But here, you're the only dribbler in the room.”

It's been three years since Rhys moved to LA to play a gay lawyer in the American TV drama Brothers & Sisters. He grew up in Cardiff, where he played Elvis Presley in a school musical, thus inspiring him to audition for RADA in London, where he was awarded the Patricia Rothermere Scholarship. The son of a head teacher and a teacher for the visually impaired, Rhys went on to appear in the BBC's Backup police drama before landing what was arguably his breakthrough role as Benjamin in the stage adaptation of The Graduate, starring with Kathleen Turner.

None of which quite prepared him for life in LA, where, in spite of his standard-issue Toyota Prius, and his LA uniform of T-shirt, jeans and trainers, he doesn't feel entirely at ease. He prefers dingy boozers to poolside terraces; he likes watching rugby, not the LA Lakers; he doesn't understand “dating”. No wonder, then, that Rhys, now 33, is so excited about his latest gig: playing the most celebrated Welshman in modern history, Dylan Thomas, in a John Maybury-directed film, The Edge of Love, scripted by none other than Keira Knightley's mother, Sharman Macdonald. As you'd expect, Rhys meticulously researched the role of the Welsh bard, whose lifestyle can be summed up by his often-quoted (but seldom fact-checked) last words: “I've had 18 straight whiskies, I think that is a record.”

The Edge of Love is vaguely based on a recent biography of Thomas, A Farm, Two Mansions and a Bungalow, and focuses on the intense three-way relationship between the poet, his bawdy, trick-turning wife, Caitlin MacNamara (Sienna Miller), and his sensitive, cabaret-singing childhood sweetheart, Vera Phillips (Keira Knightley). Interestingly, the part of Caitlin was supposed to be played by Lindsay Lohan but she backed out, for, er, “scheduling” reasons.

It's an odd film, perhaps largely because Knightley is about as Welsh as she is black. It's also a surprisingly unflattering portrait of Thomas, who is depicted avoiding action in the Second World War to instead make half-hearted propaganda films, set a world cigarette-smoking record, anaesthetise himself to the Blitz with Guinness, and put his head in the laps of his female admirers while asking to be petted like a “little dog”.Rhys says that as a boy he idolised the poet. “I loved his stuff. I even did a piece from Under Milk Wood as part of my audition for RADA. I remember the examiner saying to me [plummy voice], ‘That's rather obvious for a Welshman, isn't it?' I thought, oh no, I've f***ed the gig.”

Understandably, Rhys was terrified of getting the ultimate part for any Welsh actor (an “Oh my God moment”) only to make his boyhood hero unlikeable. “In the biographies they interviewed a lot of people who knew him. They all said he was the most loveable, pathetic, engaging, entertaining, nightmare you'd ever come across. He was childlike in his behaviour, in that there was no malice behind it. Ultimately he thought of himself as a child. I think that's what I was trying to get at in the movie, but I think at times he just comes across as a bastard.”

Still, the film isn't really about Thomas. It's about the strange friendship and tussle over Thomas's attention that went on between Caitlin and Vera. Early on in the project, Rhys suggested (drunkenly) to a Daily Mail reporter that the film would reveal a sexual element to the relationship - a claim that resulted in the set in Wales being mobbed by paparazzi hoping to catch the ultimate A-list girl-on-girl kiss.

“We were shooting a scene in which they larked around, playing with an umbrella,” recalls Rhys with a smile. “At one point John Maybury shouted, “Now kiss!” and you could almost hear the thump of paparazzi falling from the trees.”

Rhys thinks Caitlin and Vera probably weren't lovers. “Caitlin was known to have had relationships with women,” he says. “But ultimately, the two of them were in an isolated place, yo-yoing with Dylan's on-again, off-again affections, and they just found great solace and comfort in each other.”

So what was it like to work with Miller and Knightley? Rhys says they were “fun, naughty, professional and a good laugh - although both are a bit rough on the eyes day in, day out”. He remains diplomatically unforthcoming on the subject of his wellpublicised romance with Miller, which reportedly caused ructions between the actress and her then fiancé, the actor Rhys Ifans, from whom she split recently.

Fittingly, it's that same kind of jealousy that provides the most dramatic moments in The Edge of Love: Vera marries a young British soldier, William Killick, who is promptly sent to the front line, where his fellow Tommies are turned to mincemeat. When Killick (Cillian Murphy) returns as a wild-eyed veteran to find Thomas, Caitlin and Vera living as a cosy threesome, he is none too pleased. Anyone who doubts the veracity of events should talk to the film's producer, Rebekah Gilbertson - William Killick was her grandfather. Rhys says: “I loved the fact the film was so personal, and that it was a real labour of love. [Gilbertson] grew up with these stories. She'd had the dream in her head for a long time to make this film, to tell this story.”

All of which leads on to what Rhys dreams about doing with his career, having gone from the West End to TV star and now movie star. “I didn't go to the theatre when I was young, it was American movies, that's what I loved. So you think, ‘Oh, maybe one day it would be nice to do American movies.' But then I stopped having plans, because I realised that in this game you can't have them, because as soon as you do, you get disappointed. But I'll stay in LA, see the visa out. I'll stay here as long as I can.”

Does that mean he might actually start dating the locals? “No,” he says, giggling. “Here, everyone who's in a couple is obsessed with matching up single friends. Everyone's like, ‘You guys should go out on a date.' Initially you go along with it and then you realise, actually, this is ridiculous.”

So a life of bachelordom awaits? Rhys shakes his head. “I need to get married. It's time to grow up. It's just easy to forget about it in LA, because it's such a transient kind of place. But yes, I should get married - as my mother tells me every Sunday.”

The Edge of Love is released on Friday

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