As soon as the actor Paul Dano read Richard Ford’s novella Wildlife, he knew he wanted to make a film of it. More than that, it was a story that took hold, would not let him go. It may be that we all have at least one book of this sort in our lives, a story that becomes an obsession, that speaks to us in an irresistibly powerful way. It is now seven years since he read it and he has written a screenplay with his partner, the actor Zoe Kazan, and made a film – his directorial debut – in which Carey Mulligan gives the performance of a lifetime as an unravelling wife and mother, Jake Gyllenhaal plays her tormented husband, and newcomer Ed Oxenbould their bewildered teenage son. The film has already had rave reviews after its premiere at the Sundance film festival, with Variety hailing Dano as a “natural born film-maker”, while earlier this month the New York Times called it superb before concluding: “The whole of the film is a potent collaboration in every respect, and a remarkable directorial debut.” But when I meet Dano and Kazan – in London for the film festival – I want to go back to the film’s beginnings to discover why it mattered so much to them to make it.

We meet in a five-star hotel overlooking the Thames, where, in contrast to the overblown luxury of the surroundings, Dano (34) and Kazan (35) look almost as if they got here by mistake. Neither is dressed in celeb glad rags: they look more like hikers about to ask for directions to the nearest youth hostel. Off screen, they seem to will themselves to be smaller than life, as if hiding here in the hotel’s upstairs bar. As actors, they have outstanding presence. Dano is especially good at dangerous roles in which softness creates a false sense of security (There Will Be Blood, 12 Years a Slave). But he enchants, too, in more sympathetic incarnations: Pierre in War and Peace; the young Brian Wilson in Love & Mercy, the biopic about the Beach Boys. Kazan rivals this with a smart, unpredictable quality all her own (The Savages, Revolutionary Road and The Big Sick) and early on in her career was described by the New York Times theatre critic Ben Brantley as having “spiky, gamine charm” and was later praised by Ian Rickson who directed her as Masha in The Seagull for her “fierceness of intelligence and independence”. Today, their aura is studious – you would not be surprised to learn they had just spent a day in a library or were planning to head back to one directly. Kazan is wearing a loose, kindly, checked cotton dress. Dano wears a lumberjack shirt, baseball cap and horn-rimmed specs. The two of them are focused, unflamboyant and warm, what my grandmother once usefully categorised as “real people” – not always easy to come by in showbiz.

But there is something I need to ask before we chase Wildlife further – there have been rumours that they have managed not only a new film but a new baby – a daughter, thought to have arrived on 31 August. Vanity Fair announced the news but could not confirm it. The New York Post’s celebrity gossip site Page Six reported that the baby had been named Alma Day but followed this with the couple’s “no comment” (mum really was the word). The only public hint of the baby’s existence had been Kazan’s veiled tweet, at the end of the summer, saying: “Honestly, this fall is already an embarrassment of riches for Paul and me, and it hasn’t even really started yet.” I ask them directly: are they parents to an imaginary baby? And they look at one another and smile and say: “There is a real baby.” And Paul adds: “That’s why I have my phone on. I’m checking on the sitter.” They add that they flew in from Los Angeles a few hours earlier that morning and are very tired, jet lag compounded by the zombiedom of new parenthood. Their tiny daughter, Kazan says, received compliments as they left the plane on her quiet demeanour (further proof that she excels at keeping her existence secret). Back home in the US, Kazan volunteers, they are getting a lot of help with childcare from her parents.

“But it’s a strange period, because we’re putting Wildlife into the world and I’ve just made a Coen brothers film [The Ballad of Buster Scruggs – she plays a frontierswoman in the 19th-century wild west] and Paul is in a Showtime mini-series [Escape at Dannemora] coming out very soon. And we’re trying to navigate being new parents. We’re both supposed to be not working right now but we’ve had to make some exceptions…” As she speaks, Dano occasionally pats her knee affectionately – the reassurance, one guesses, sweetly unnecessary because, even exhausted, Kazan comes across as someone who knows her own mind and how to speak it. From time to time, they turn to look at one another – familiar collaborators – as if used to batting questions to and fro – conversation as sport.

It is inevitable that family – parents and children – should be our subject. Wildlife is one of Ford’s earlier works – published in 1990 and set 30 years earlier in Great Falls, Montana, on the edge of the Rockies. When Jerry Brinson loses his job at the local golf club and goes off to fight a forest fire – employment for the desperate – his wife, Jeanette, despairs at what she may imagine to be the end of regular family life and makes advances towards a strange, lame, old guy – a wealthy widower named Warren Miller (Bill Camp perfectly catches the character’s unnerving benevolence).

I read Ford’s little masterpiece before meeting Dano and Kazan and found that the book’s tension builds like the smoke it describes coming ever nearer the town. You feel more and more unsafe on the part of the teenage narrator: there is a dance between what he knows and does not know that keeps you reading. The challenge of turning the book into a screenplay is clear: Joe almost watches his parents’ life as if it were a film. He says very little. I suggest that it is a novel about helplessness, and Kazan and Dano do not disagree.

“When I read Wildlife, I felt it was written for me,” Dano says. “I had a profound emotional reaction. The first step was to ask myself: why am I feeling this way? We looked at the feeling behind the internal monologue and thought about how to turn it into an action or an image.” But could he answer his own question? Why did the film speak to him as it did?

The answer emerges slowly: Dano’s father was a businessman and the family lived, for the first few years of his childhood, in a one-bedroom apartment in Manhattan. There was lots of love but “turbulence” too. The family was “close, but sometimes that closeness was too close”. He adds, blushing slightly, that his parents “had their struggles”. He has a sister two years younger and a brother 16 years older (with whom he did not grow up). “I was like Joe – I didn’t act out, I wanted to keep things together.” He believes Ford explores the “mystery of who parents are” and this he found intoxicating. Like Joe, Dano was required to move – in his case, to Connecticut – aged 14. “Your home is the world… I identified with this kid being thrust into adulthood.” But what he most cherishes is Ford’s proposition that family love is permanent against the odds.

Kazan’s family background was completely different from Dano’s and more “classically harmonious” (she has talked in interviews about her closeness to her only sister, Maya). “Yet all families have their struggles, and mine is no different.” She grew up in Los Angeles, daughter of two high-flying screenwriters – Robin Swicord (who adapted Little Women, Matilda and Memoirs of a Geisha) and Nicholas Kazan (who was Academy-nominated for his screenplay for 1990’s Reversal of Fortune) – and is the granddaughter of Elia Kazan, the director of On the Waterfront and East of Eden (and controversial because he identified former colleagues as communists during the McCarthy era).

Zoe Kazan had already written stage plays (notably Absalom – about complicated father-child relationships) and the screenplay for Ruby Sparks, a well-received 2012 fantasy romance starring her and Dano, before taking on Wildlife. I ask whether she learnt screenwriting by osmosis? “Not even osmosis. My mom is obsessed with structure. Even when I was a little kid, my parents would pause movies and explain, from a craft perspective, what had just happened. They gave me their scripts [of the children’s movies they had made] to read when I was five. Even the scrap paper in my house was recycled scripts.”

Carey Mulligan in Wildlife. Photograph: AP

But Dano was first, between jobs, to try to write the film version of Wildlife. He showed it to Kazan, who admits: “I felt crazy reading it.” Charmingly, Dano eggs her on to say precisely what was wrong. And she continues: “It was not in screenplay form. He had images in his brain. There’d be a scene with no dialogue in which he had written: ‘They sit round the table and talk about the weather.’ I’d say: ‘What is this?’ He would explain: ‘The camera is outside. You don’t hear the dialogue.’ The screenplay was unreadable to anyone who could not read Paul’s mind. I gave him lots of notes, but five pages in – it was not going well. I eventually said: ‘I think you should let me take a pass at this because it will just be faster and better.’” And they explain the process that evolved: they would write separately, edit one another, write again.

The film is shot in an untricksy way, as though to salute Ford’s transparent prose. “I’ve always been someone who likes things to be spare, honest,” says Dano. “I like the illusion of simplicity – things that look simple but are complex.” And this includes the weight of silences in the film – cinema’s equivalent to reading between the lines. But in terms of the writing, Dano insists Zoe is the “proper writer”.

Kazan’s help went further than words. When their money came through to make the film, she was in Mike Bartlett’s Love, Love, Love off Broadway and so missed the filming, but stayed involved. Among other things, she was the fabric consultant – not the trifling role you might suppose. There is a pivotal scene where Carey Mulligan wears what her character unforgettably describes as a “desperation dress”. Dano sent four different fabrics to New York for Kazan to consider. “We’d had a very different green in mind but the moment we saw the poison green, we thought: great. It was so outside the colour palette of the film. With little time or money, our costume designer did amazing things.” The viciously green silk dress is a drama in itself, in which Mulligan looks at once sensational and precarious.

During the 28 days of production, what Dano aimed at was an atmosphere in which everyone – and it especially mattered to him that the crew felt included – was “in tune” and understood the story’s strange atmosphere, best summed up in a passage of Ford’s own words, which begins with the description of fire engulfing a tree:

“A spark had found it, and it exploded in a bright, steepling yellow flame that leaped and shot out bits of fire into the night toward other trees, and swirled its own white smoke, flaming and then dying quickly as the wind on the hillside – a wind that did not blow where we were – changed and died. It all happened in an instant and I knew it was dangerous though in a beautiful way. And I understood, just as I sat there in the car with my mother, what I thought dangerous was: it was a thing that did not seem able to hurt you, but quickly and deceivingly would.”

The sound of fire is essential and frightening to the film: its crackle, gobble, roar and Jeanette’s brittle question rising above it: “Do you like it?” to which Joe replies: “No.” Kazan and Dano explain they were lucky to have had extensive advice from a friend who had worked as a volunteer fighting wildfires in the US.

As they talk, they seem two of a kind – super-intelligent, offbeat, likable. And there are parallels in their showbiz trajectories. Straight out of Yale, Kazan was spotted by an LA agent at 24. Dano also never had to fight for work: he started his professional career, aged 11, on Broadway. “Someone asked me to do a regional play – a manager saw it and told me to audition for Broadway.” The couple first met acting in Jonathan Marc Sherman’s play Things We Want (2007). Kazan played an alcoholic concert pianist, Dano one of three dysfunctional brothers. They have since found that the difficulty about working together is ringfencing private time. Kazan recently announced a resolve not to act together any more. Dano says: “You might be on set 12 or 14 hours and then go home together. You’re not going to write for 12 hours. We’d talk for hours – but never wrote in the same room.”

They seem like soulmates – how similar are they as characters? “Not at all! We meet in what we love, but are incredibly different,” Kazan says.

“Obviously, we get along, we like each other,” Dano adds in his friendly way. “But Zoe is fast and I’m slow.” “Paul’s gut instinct is to try every possible permutation before he decides on something. I’m more extroverted. He’s more patient. I like to run into the ocean, he likes to watch me run.”

“Zoe is a good multitasker… I can’t do more than one thing at a time.”

Early on, Richard Ford urged them to make the story their own, suggesting they leave his story where it was “safest” – on the page. Their worry was that, in the end, they might have been too faithful to the novel but, to their huge relief, Ford has given the film the thumbs-up. I tell them I am not surprised. And I ask what they would like their audiences to feel as they leave the cinema. Kazan says: “We just showed the movie in LA and had critics and friends whose parents split up in tears.” “People have had memories return,” adds Dano.

“That means a tremendous amount to us,” says Kazan. “You make any piece of art hoping someone might receive it in the way Paul received Richard Ford’s book – as if it were made for them.”

And how has this experience left them? Is there an appetite for doing more? Paul is about to appear on Broadway in Sam Shepard’s True West, but is in no doubt: “I definitely want to do more direction. I can’t wait to make another film. I just don’t know when that will be.” Might they need to leave it while baby Alma has a moment or two in which to grow up? “Yes!” they exclaim in unison.

Wildlife is released in the UK on 9 November