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.”

Guy Lodge is a South African-born critic and sometime screenwriter. In addition to his work at In Contention, he is a freelance contributor to Variety, Time Out, Empire and The Guardian. He lives well beyond his means in London.