How serious is Jake Gyllenhaal about acting? Well, the 35-year-old actor and Oscar nominee (for Brokeback Mountain) spent five months in the back of a police car, on ride-alongs with the Los Angeles police to get in character for the 2012 cop film End of Watch. He lost 40lb by eating nothing but kale salads and running 15 miles a day for six months to play a skeletal video journalist in 2014’s Nightcrawler.

He trained so hard for last year’s boxing movie Southpaw, working out six hours a day for five months (including 2,000 sit-ups a day), that he decided his girlfriend at the time, the model Alyssa Miller, was getting in the way, so he dumped her, preferring instead to focus . . .

“No, no, no! That is just not true!” Gyllenhaal interrupts, half-giggling with embarrassment. “Look, I love my work, but my life comes first. I was intensely focused when preparing for that movie, yes. But, no. Haha. No.”

Miller-split aside, Gyllenhaal will say nothing else to undermine the notion that acting is, for him at least, close to sacred: transformative, cathartic and boasting an important social and political function (he’s on a mission from President Obama — more on this later).

The odd thing is, he’s strangely convincing. Gyllenhaal is dressed, incongruously, like a Latino gangster, in grey plaid shirt, buttoned to the neck, while his blue Bambi eyes are mostly on full beam. He is smart (he studied eastern religions at Columbia University), sometimes circuitous (“My mind works — and maybe you can tell from our conversation — in an abstract way”), and sometimes completely off the page (“I wish I was Irish because I have a deep love for potatoes”). He is also self-deprecating enough to know when he sounds like a luvvie (“Putting aside pretension, which I know I can so easily be accused of . . .”).

For now, though, he wants you to know that he is fundamentally an artist, and that for the past four years, exactly, he has been choosing roles with precision. The results speak for themselves — award-worthy movies (see Southpaw, Nightcrawler, End of Watch) featuring towering performances in stories that are entertaining, but with an intellectual edge. “I know what type of stories I want to be involved in now, and what kind of artist I want to be,” he says. “And that’s important.”

The apotheosis of the new and improved Gyllenhaal method would seem to have arrived with his latest movie, Nocturnal Animals. Written and directed by Tom Ford (his first film since A Single Man in 2009), and featuring Gyllenhaal in the dual roles of a novelist and his own fictional protagonist, it is indecently good. It won the Grand Jury Prize at this year’s Venice Film Festival. The Hollywood Reporter called it “a ceaselessly gripping stunner” and Oscar buzz abounds.

It is a film that leaps, with breathtaking aplomb, between three narrative planes, interweaving the stories of Gyllenhaal’s writer Edward and his wife Susan (Amy Adams) and their early relationship in New York, with that of Susan’s empty, post-divorce and remarried life in contemporary Los Angeles, as well as, crucially, the unfolding and often terrifying fictional reimagining of their relationship in the pages of Edward’s novel. Here he is transformed into Tony, the victim of a life-changing roadside encounter with a savage homicidal Texan hick, impeccably played by Aaron Taylor-Johnson.

Much of the pleasure of the Tony tale is built around the almost palpable enmity that fizzes and pops between the screen rivals Gyllenhaal and Taylor-Johnson. Did they, in real life, go for a beer after work? Gyllenhaal looks appalled. “I try, as much as I can, on a movie set, to create an environment where some real feelings can come out,” he says, diplomatically. “And I will say that Aaron is a lovely man. But when it came down to shooting the movie, we were not buddy buddy, I did not spend much time with him and, no, we did not go out for a beer afterwards.”

Of the Oscar buzz he is equally circumspect. “When people talk about your movie that way, of course you’re going to get excited, and it’s a lovely feeling to have. But, really and truly, all I care about is that I get to go back to work the next day.”

The film is a swirling mass of themes, ideas and incident. It’s about the gruelling interpenetration of biography and fiction, the hollow pursuit of wealth, the emptiness of much contemporary art and the difficult primal fractures that exist, and slowly expand, in all romantic relationships. Susan, with prompting from her disapproving mother (Laura Linney — fabulous), thinks that Edward’s emotional sensitivities mean that he is fundamentally “weak”. Gyllenhaal, as someone clearly in the sensitive camp, attacks this idea. “Being a man, the ability to love and be vulnerable is probably one of the strongest things we can do,” he says, clearly peeved. “But this question comes up all the time, in terms of what people consider to be attractive — they think that vulnerability is weakness.”

Mostly, however, he says, “what the movie is really about is the difference between the choices we make when we want to look good and look right, and the choices we make when we know what actually is right”.

This is an idea close to Gyllenhaal’s heart, reflecting his career epiphany, in 2012, when he turned away from Hollywood. Back then, despite the critical acclaim received from Brokeback Mountain and other grown-up films such as Jarhead and Zodiac, he was clearly being groomed for Hollywood mega-status.

He was born into a solid Tinseltown lineage; his father is the director Stephen Gyllenhaal (Paris Trout), his mother the screenwriter Naomi Foner (Bee Season), and his sister the actress Maggie Gyllenhaal (Secretary). As a child he went car-racing with his godfather Paul Newman, and shared a house with the director Steven Soderbergh (he lived, briefly, in the Gyllenhaals’ spare room). He began auditioning for screen roles at 12 — “from 12 to 20 I had the journey that most actors have when they graduate from drama school” — and delivered accomplished turns in films ranging from October Sky to Donnie Darko and Proof. It was inevitable that he graduate to the A-list.

And so he was cast, in 2010, as a floppy-fringed, pumped-up, fake-tanned beefcake hero, the star of Disney’s $200 million wannabe action franchise Prince of Persia: The Sands of Time. The film was a critical disaster (“Mush,” said The New York Times) and a box-office disappointment. He followed it with another blatantly commercial project, this time in suave, populist, Cary Grant mode, as a Viagra salesman in the romantic “dramedy” Love & Other Drugs. That was a shocker too. I met Gyllenhaal on that film’s promotional trail, in late 2010, and he was miserable. We had a tense interview during which he tried to make it sound interesting, and I tried, not very enthusiastically, to agree.

He says today that he eventually reached breaking point. “I didn’t want to do another interview where I had to talk about a film that I didn’t truly love. I had veered from who I am, as a person. I got sucked up into that machine. I had lost my way.” The solution presented itself, gradually, over the next year. He moved from LA to New York, forced himself to be bold and regard himself as “an artist”, did a film that he loved (End of Watch), and took some professional advice from the most powerful man on the planet.

About this time, Gyllenhaal was in Washington and asked about a tour of the White House. “I get a phone call saying that I should come, and probably wear a suit. I got an inkling that I wasn’t going to get just the normal tour.” He says that the meeting with President Obama in the Oval Office was short, but overwhelming, and that during their exchange the president said: “Your job as entertainers is to provide entertainment and, given the tough times that we live in, to create art that says something.” As if by magic, the films that Gyllenhaal has done since have easily lived up to that presidential remit.

Off screen, Gyllenhaal remains a New Yorker, appearing on and off-Broadway (he starred opposite Ruth Wilson last year, in Nick Payne’s Constellations, and appeared this week in a three-day run of Stephen Sondheim and James Lapine’s Sunday in the Park with George, to critical acclaim), and with a love life that seems, at best, perpetually in motion (from Kirsten Dunst to Reese Witherspoon to Taylor Swift to Miller). Of his romantic status today he’ll only laugh and say, “I’ll leave that up to you. Fictional or nonfictional, you write whatever you want. You have all the power.”

There are more movies on the way, full of meaning and entertainment value. They include an inspirational tale from the Boston marathon bombing, called Stronger (Gyllenhaal plays the survivor and double amputee Jeff Bauman), and a tale of intrigue aboard the International Space Station, Life.

He wishes, perhaps inevitably, that he could do a comedy. But he knows that, before then, he needs to lighten up.

“Seriously, why don’t I?” he asks, laughing. “I should, but I f***ing don’t know why I can’t.” He chuckles and adds, tongue perhaps only slightly in cheek, “I get tired of taking myself so seriously.”

Nocturnal Animals is released on Friday.