Greta Gerwig: The queen of low-budget cinema is breaking into the mainstream with her role in Arthur

The first sign that Greta Gerwig may not be your average movie star comes as I'm striding into the lobby of the Four Seasons hotel in Beverly Hills, 45 minutes before our scheduled rendezvous. My mobile telephone rings. Would I mind coming straight up to Greta's suite? She is running rather early, would hate to intrude on more of my Friday afternoon than absolutely necessary, and so wonders if we can crack on. Yes, you heard that right: a Hollywood actress is managing to be vaguely considerate towards another human being AND to not be late.

A second sign that Greta Gerwig might plough her own furrow comes shortly after we sit down to discuss her new role, as Russell Brand's love interest in a remake of Dudley Moore's 1980s classic Arthur.

She auditioned for the film, she reveals, after learning that it was being scripted by Peter Baynham, the British screenwriter behind Alan Partridge, who is pretty much her favourite TV character, ever. She describes Partridge, whose charms are almost always lost on her fellow Americans, as "fucking genius!" – a nice turn of phrase, but not very Hollywood.

All of which is par for the course for the 27-year-old Gerwig, who crept into the world of celebrity via the back door. A long-time darling of an ultra-low-budget brand of indie film-making known as "mumblecore", she went mainstream last summer after being cast in the hugely under-rated Greenberg, co-starring Ben Stiller. Her turn as Florence, the female lead, attracted admiring reviews, and won her a supporting part in Ashton Kutcher and Natalie Portman's spring comedy No Strings Attached. Now Arthur, her biggest break yet, will see her share top billing with Brand, Jennifer Garner, and Helen Mirren.

"It does feel a lot like I have kind of, um, snuck into the castle," she says, with regard to the past year of her life. "I mean, movie stars are today's version of royalty, so it's completely surreal that I should now be appearing next to them. The posters for Arthur are all over New York, where I live, and it's scary: you can't miss them. I've even seen myself go by on the side of a bus, which was crazy. The whole thing feels incredible. It's thrilling. I think, well, I couldn't have really dreamt it up."

To her growing army of male admirers, Gerwig is what you might call girlfriend material: pretty, rather than classically beautiful, intelligent, and fearsomely cultured. Her hobbies, she says, consist of visiting museums, galleries and theatres, and in down-time, reading (she's currently working through EM Forster's back catalogue). Female fans, meanwhile, see Gerwig as a sort of ideal best friend – and greatly admire her ability to unflinchingly portray the travails of twentysomething modern women.

In Arthur, she plays Naomi, a cute-but-impoverished New York tour guide, who captures the heart of a well-known squillion-heir socialite called Arthur, who is played by Brand. The plot premise is closely modelled on the 1981 original. Where Sir John Gielgud was the leading man's butler, Mirren fills in as his nanny, Hobson. Jennifer Garner is Arthur's upper-crust fiancée. Geraldine James is the pearl-wearing matriarch who continually threatens to cut off Arthur's inheritance.

It's a moot point, of course, as to whether this movie (by anyone's money, one of the great comedies of its era) really needed to be remade. Brand is no Dudley Moore. Not yet, at least. But he certainly has moments. There's a decent quota of slapstick, the narrative can be pleasingly unpredictable (when it isn't being overshadowed by the endless product placement which seems de rigueur in modern studio comedies) and the film's central point – that enormous wealth doesn't necessarily buy you happiness – feels topical, given recent economic history.

But the best thing about the film, perhaps the one thing that means you really should watch it, is Gerwig. She becomes its heart and soul: at turns sensitive, confused, winsome, and expressive; more complex a figure than she needs to be, but ultimately more believable.

As established fans will already be well aware, there's a terrific matter-of-factness about her acting, and a genuine vulnerability, which adds psychological depth to characters which on paper have no right to possess it. Recently, she's been gaining her plaudits in all the right places, and appearing on those "young Hollywood" lists we're all supposed to notice.

"I find acting's one of the spontaneous art forms," is how she explains her much talked-about naturalistic approach. "It's like playing live music ... You can prepare for it and you can practise, but if something really magical is going to happen, then it just does, in the moment."

In an industry that tends to celebrate showy performances, her most noticeable attribute on screen is a tendency to underplay. That's a rare approach. But she says: "It never felt that the way I acted was different to what other people were doing until someone actually told me, 'I think you're doing something different'."

Critics love this kind of originality. That's why some have pegged Gerwig as a method actor in the noble tradition of Marlon Brando. Others have remarked how she can leave you, days later, mulling over her performance. If Arthur is a hit, and the mass-market cottons on to her appeal, the sky could be the limit. Not long ago, AO Scott of The New York Times, perhaps the most influential film reviewer in the USA, devoted his entire column to an appreciation of her talents.

"Ms Gerwig, most likely without intending to be anything of the kind, may well be the definitive screen actress of her generation," he wrote.

"She seems to be embarked on a project, however piecemeal and modestly scaled, of redefining just what it is we talk about when we talk about acting."

When I mention Scott's hagiography, Gerwig smiles awkwardly and fiddles with her hair, which is something she does a lot. Choosing her words hesitantly (which she also does a lot), she then claims to have only read half of the 2,000-odd word article, which came out last summer. Asked how various plaudits made her feel, she employs just the right amount of modesty. "It just feels nice," she says "to be part of the conversation."

This, it turns out, is typical Gerwig: gentle understatement is as much part of her personality as of her acting. During our time together, she curls up on a sofa, in a manner that suggests someone in need of tea and biscuits. Having spent the morning in make-up for photographers, she is impeccably groomed (and is still wearing a stylish D&G dress, chosen for a magazine shoot). But her default setting is spontaneous, a fact which helped her win the role in Arthur: during four rounds of auditions, she was asked to improvise comic scenes with Brand. "He's smart and funny, so that worked."

A knack for improvisation also helped kick-start Gerwig's early career. The youngest of three children, born into a happy middle-class family in the unlovely Californian city of Sacramento (mother Christine was a nurse, father Gordon a computer programmer) she began treading the boards in school plays during her teens, and pursued the profession while studying philosophy at Barnard College in New York in the early Noughties. After graduating, and having become established in what you might call luvvie circles, she became friendly with Joe Swanberg, who became a prominent player in the oft-maligned genre of film-making known as "mumblecore".

The term, perhaps more talked about among the commentariat than by real people, refers to films made with tiny budgets, in which cast and crew will typically take over a small venue for a number of weeks, creating a narrative as they go, and later editing vast amounts of footage into a coherent film.

Sometimes it works; other times, it's a mess. Two of her best efforts, Hannah Takes the Stairs (2007) and Baghead (2008) got good write-ups, and minor distribution deals. The rest proved to be more of a minority taste, but nonetheless helped Gerwig gain a solid following among cultish devotees of the genre.

In 2008, after generating sufficient buzz on the indie circuit, she acquired a Hollywood agent, and with it a chance to make an actual living from a trade which she'd previously financed by tutoring the children of wealthy New Yorkers ("You can make a lot of money teaching rich, stupid kids," she remarks).

Shortly afterwards, she won the part in Greenberg, and the rest has been a whirlwind that has seen her treading red carpets and turning up on the hallowed sofas of David Letterman and his late-night peers.

The trappings of success haven't stopped Gerwig staying true to her method-ish, mumblecore roots. To prepare for the Ben Stiller movie, in which she played a wealthy family's personal assistant, she spent a fortnight in Los Angeles, working as an actual PA. For Arthur, she tried a similar trick.

"Even if I'm playing a character who's not like myself, I try to become very much like them over the course of a shoot," she says. "So for Arthur, my friend Ted is a tour guide in New York, and I went round with him before we started shooting, to get an idea of what he does."

Her next film, out later this year, is a smaller independent title called Damsels in Distress, which co-stars Adam Brody (from The OC) and demonstrates that for all the growing fame and fortune, she's not fallen out of love with small movies. In the meantime, she's hoping recent events aren't some dream from which she's about to wake up. For now, she still lives the single life in New York, in a shared flat.

"The best thing about these studio films is that they bring me to LA for the launch," she says. "It means my mum and dad can drive down the six hours from Sacramento, and stay in the suite, too." As Gerwig's learning, Hollywood stardom can have its perks, if only you know how to exploit them.

'Arthur' is in cinemas from Friday