For someone who has already won a BAFTA, been nominated for an Oscar, trodden the Broadway boards and worked with such singular filmmakers as Steve McQueen, Baz Luhrmann and Michael Mann – all with years to spare before her 30th birthday – you wouldn’t think “unattainable” is a word that often enters the mind of Carey Mulligan.

Yet that’s exactly how the British actress regarded the prospect of working with the Coen brothers – perhaps the most enduring offbeat members of America’s current filmmaking establishment – before they approached her for a small but viciously significant role in “Inside Llewyn Davis,” their melancholy, elliptical journey to New York’s folk music scene of the early 1960s.

The actress is a longstanding fan of the duo – “Fargo,” at least until “Davis,” was her favorite of their works – but was thrown for a loop when she was selected to play Jean, the scaldingly caustic ex of Oscar Isaac’s shambling title character, with whom he has some crucially unfinished business. And it wasn’t just because of the against-type nature of the part. “I just never imagined I”d be in a Coen brothers film,” she says. “You know the actors that get to be in their films, and they’re brilliant. I’m not one of those actors. So just getting the email with the script – and it said at the top ‘a Coen brothers film’ – was incredible.”

So, she thought upon actually reading it, was the script. “Honestly, I was just so happy to read a female character who was given more than a few words strung together,” she laughs. “But such words, in her case. To be given whole paragraphs of that kind of vitriol was sort of amazing. Everyone has a temper, but I don”t think I”ve ever reached that level.”

Jean is the most high-temperature character in a film otherwise very much in a Coens shade of cool. She gets much of the script’s quickest, most verbal comedy, but also its blackest, most unruly reserves of feeling – a refreshing register for an actress often called upon to play more demure, sensibly guarded individuals, be it the precocious, well-spoken teenager of her breakthrough film “An Education” or the fine-china delicacy of F. Scott Fitzgerald’s Daisy Buchanan. For Mulligan, it was an opportunity to don the disguise of a character bearing precious little resemblance to herself, while still finding ways to empathize with her.

“She has so many brilliantly written lines, and they’re so much fun to deliver, and that’s the unmistakably the Coens, of course,” she says. “You could only dream of coming up with that stuff on the spur of the moment. At the same time, however, there are glimpses of a real relationship behind it, and that’s what Oscar and I worked on. These people, genuinely in pain, who genuinely feel for each other but kind of can”t see past all the dirt that”s come their way. The only way you can be so incredibly unpleasant and brutal to someone is if you have a real intimacy and a history. Llewyn is who she really is herself around. So, ugly and not very nice. But honest.”

That’s the measured, sensitive answer, of course. She goes on to explain that and Isaac devised an entire back-story for the ex-lovers. (“It wasn’t particularly sophisticated,” she allows, before giving a potted history of their “drunken slip-ups.”) But that’s not to say onscreen anger doesn’t offer more immediate pleasures: “It’s just so fun to scream at the top of your lungs, at seven in the morning in Washington Square Park, at an actor that you love acting with.”

Mulligan’s affection for Isaac dates back to their experience playing husband and wife – to less raw emotional effect – in Nicolas Winding Refn’s sleek neon thriller “Drive.” Her familiarity with him, and the non-prescriptive nature of the Coens’ direction, she says, encouraged her to “let loose” in ways she hadn’t before. “I assumed they would reign me in,” she says, “but more often than not, they pushed me further and made her more brutal, meaner, harsher. But they”ve entrusted you to play a part and you”ve put all your faith in them in turn. And I felt that comfort with Oscar too: he”s a friend and a great actor, so I got to spar with him.”

Sparring with the Coens, however, was slower to come: Mulligan first met with them by phone and admits her nerves put paid to any future memory of their conversation. “They just kind of said a bunch of things on the phone for, like, 15 minutes, and they were kind of laughing the whole way through” she recalls. “I was in LA doing practice for ‘Shame,’ so I didn”t meet them until the following year, when we came together to rehearse the music.”

By that point, she’d completed both “Shame” and Baz Luhrmann’s gaudy, glittering adaptation of “The Great Gatsby”; it took some time, she says, for her “head space” to catch up to the new project. “Nothing about the entire film was remotely stressful to do,” she enthuses. “I”ve never had that on anything. I”ve done jobs that I”ve absolutely adored and there have been really, really difficult ones. But this was just so fun, so freeing. That’s what the Coens set up for you as an actor, just by being who they are. The great thing about them is that when you’re filming, you don”t feel the labor or the art or the set ups or the design. Everything moves so quickly and is so planned out: the world that they created is there, so you just don”t really think about it.”

“There was something really cathartic about it after ‘Gatsby,’ which was a great experience, but a big, big, big film – very visual in a way that I wasn”t used to,” she continues, and she’s not just referring to the film’s own mise-en-scene.

“I”d never played a girl that was meant to look pretty before. I played girls that were just girls; I”d never played a character that had all these fantastic descriptions of her beauty. That was something that I had to tackle in ‘Gatsby.’ So going to the Coen brothers and playing this girl who doesn”t wear makeup and has a big ill-looking face and black wig – just, generally, looking kind of crap – was wonderfully liberating. There”s no vanity to her. it”s quite a feminist idea.”

 “Inside Llewyn Davis” also required Mulligan once more to exercise the singing chops she demonstrated in a famously torchy, slowed-down version of “New York, New York” in “Shame.” The Coens’ film required her to adopt the more distinct vocal style of Greenwich Village folk, but the actress found this is a different experience in other respects too.

“‘Shame’ was a very different experience because that scene was really sort of a message to her brother,” she says. “This is so light and, after my initial nerves, so much fun. We kind of figured out our little trio and our homage to Peter, Paul and Mary. And T-Bone Burnett was incredible the whole way through – not just for the singing but through filming. He’s a lovely person to have around. He gave me confidence to do it.”

Burnett, of course, wasn’t the only person Mulligan could turn to for some musical encouragement. Her husband is Marcus Mumford, frontman of Grammy-winning folk-pop band Mumford & Sons – who was attached to the film in a musical capacity before Mulligan came on board. “I”m mostly influenced by the music that we listen to at home,” she says. “I”m not a massive music fan, actually – I mean, I am not an expert. I have such broad taste: from really cheesy pop rubbish that I listen to in the gym to decent music that I”m exposed to by my family.

“We had a great week before we started filming, just working on our comfort levels with the other actors and the music – just people hanging around and playing guitars and being creative, and me, sort of sitting in a corner watching. There”s something really enviable about musicians: they have this effortless sense of community. People can walk into a room having never met, pick up a musical instrument and start playing and they”re already together. They”re already sort of united by it, which is not the same with acting. It would be kind of awful if it was!”

For her part, Mulligan is choosing her jamming partners pretty carefully, admitting that she “hasn’t felt a need” to work at every given opportunity: “I’ve waited for the right things to come along, and I”m so lucky at the moment to be able to do that,” she says. “Things work best for me when I”m playing a part because I can”t bear the idea of anyone else playing it. I don”t want to do anything where I”m sort of half-arsing it.”

She has just completed shooting on Danish director Thomas Vinterberg’s new adaptation of “Far From the Madding Crowd,” and is plainly excited about it: “He’s such a brilliant filmmaker,” she gushes. Mulligan is building up an impressive portfolio of director collaborations: she actively sought the role in “Drive,” a project for which she was an unlikely fit, based on her enthusiasm for Nicholas Winding Refn’s previous work. Similarly, she pursued “Shame” director Steve McQueen based on her admiration for his debut.

She admits that, for the right director, she’s willing to take a leap of faith even if the role or script might not call out to her otherwise. “I get really swept up in people”s work, and the notion of what being in one of their films is. Like, the Coen brothers, I wouldn”t even have neded to read the script. I’d have played a tea lady. Some filmmakers, it’s a no-brainer. With the right person at the helm, even if it”s not your dream role on the page, it can get somewhere really interesting.”