Leonardo DiCaprio has come to London on what seems to be a sophisticated middle-aged gentleman’s cultural tour of Europe. First stop, Bologna, Italy, for Radiohead, where, I point out, the band did their only performance of the Romeo + Juliet song “Talk Show Host” on the recent tour. Was that for DiCaprio?

“I don’t think so,” he says. He hums the riff. “You know, I’m just thinking about it.” It seems the penny has dropped. “Yeah, that’s right.” Then he flew to the UK for the Peter Doig exhibition at the Serpentine and the Kerry James Marshall at the Royal Academy.

“That was cool,” DiCaprio says, beaming, of the latter. He is dressed in smart black trousers and immaculate white T-shirt as he whirrs a coffee machine into life in a suite at Claridge’s. “But other than that? Mostly just restaurants.”

It’s very different to the world he grew up in, in parts of Los Angeles that are trendy now but were rough back then. “Really hardcore places,” he says. His parents — George, a comic book artist, and Irmelin, a legal secretary — were “bohemian in every sense of the word” and divorced when their son was one. The family stayed close but it wasn’t an easy childhood and when DiCaprio needed to escape he headed to the corner of Hollywood and Sunset, to the Vista Theatre, a gorgeous 1920s cinema that made him fall in love with the movies.

Flexing his acting muscles: Leonardo DiCaprio in 1990.

He remembers the place as being “like a record store”, full of magic that made him want to be on the silver screen: the “great modern art form”. He started acting in his teens, in adverts, then moved into film — at 19 he was Oscar-nominated for What’s Eating Gilbert Grape, then came Romeo + Juliet, then Titanic.

Yet now? That enchanting world of the movies is under threat, DiCaprio, 51, says. “It’s changing at a lightning speed,” he says with a sigh of the medium that made him. “We’re looking at a huge transition. First, documentaries disappeared from cinemas. Now, dramas only get finite time and people wait to see it on streamers. I don’t know.” He shakes his head, a rare worried break from his Californian cool. “Do people still have the appetite? Or will cinemas become silos — like jazz bars?”

We are joined by Paul Thomas Anderson, the director of masterpieces such as There Will Be Blood, The Master and 2025’s best film, One Battle After Another, a cocktail of epic blockbuster and art house movie about a washed-up stoner in a dressing gown (Bob, played by DiCaprio) on a mission to save his daughter.

The film ebbs and flows, packed with flawed characters and exhilarating car chases, wit and sadness — exactly like the signature movies of the 1970s. I join them on an awards push — it has eight Golden Globe nominations, and Oscars and Baftas will follow. But with Netflix bidding to buy Warner Bros and send its films straight to streaming, both the director and the star are concerned that something this original and well funded will never be made again.

Master and commander: DiCaprio and Paul Thomas Anderson during a Q&A following a screening of One Battle After Another in September of last year.

“It’s hand-to-hand combat,” Anderson says, about the push of Netflix’s Ted Sarandos to shift viewers out of cinemas and towards his subscriptions, threatening cinemas more than TV, VHS or piracy ever did.

One Battle After Another resisted the fast buck of home entertainment rentals for the big screen, taking $204.7 million at the global box office — impressive for a near three-hour movie, but far less than the estimated $300 million needed to break even. It had a reported budget of up to $175 million.

The film is made by Warner Bros, so would be under the control of Sarandos. I read DiCaprio a quote that Michael Caton-Jones, who directed DiCaprio in his breakthrough role in This Boy’s Life, told him on set: “Pain is temporary — film is forever.” But is it? How can a film on Netflix stand out when it is swiftly usurped on the algorithm by reality TV or true crime slop? How can something be forever if nobody knows it is there?

“I just hope enough people, who are real visionaries, get opportunities to do unique things in the future that are seen in the cinema,” DiCaprio says. “But that remains to be seen.”

In the film DiCaprio tears through comedy to paranoia in the space of a scene, with a manic energy evident in his best work, which has earned him an Oscar and three Golden Globes. But one for giddy small talk DiCaprio is not. Mention anything outside of films and it can be rather like speaking to a particularly good-looking brick wall. When we met in 2013 I told him something catty George Clooney had said about him and DiCaprio just took a long suck on a vape before saying: “I don’t talk about people in the press.”

Which is fair. But in 1994 DiCaprio said, “I have no idea what people think of me” and I don’t think the public know him any better now. When I try to ask something even a little personal, about his youth, he simply answers a different question, tumbling into a monologue about a collaborative approach to filmmaking.

So he wants his work to do the talking and, on film, he becomes locked in. DiCaprio and Anderson nearly collaborated 30 years ago — the director offered the actor the lead in the porn epic Boogie Nights, which eventually went to Mark Wahlberg. DiCaprio “regrets” turning it down. “I’d put the soundtrack of that movie on and drive around Los Angeles, playing the blues of how much I love that movie.”

But history had other plans — he was already signed up to Titanic. In the three decades since he has barely put a foot wrong. While his 1990s heartthrob rivals, Clooney, Brad Pitt and Johnny Depp, have made dozens of flops, DiCaprio has barely a dud to his name.

That sinking feeling: DiCaprio and Kate Winslet in Titanic.

“I could argue with that,” DiCaprio protests, but I am not sure he could. Even his dullest movie, a 2011 workmanlike J Edgar Hoover biopic, J. Edgar, has its moments and Anderson agrees — DiCaprio’s CV is ridiculous: he is the Lionel Messi of acting.

“He has a commitment to not just doing any old movie,” Anderson tells me. Working with Martin Scorsese, who has directed DiCaprio in six movies, from Gangs of New York to The Wolf of Wall Street, brought “a high level of quality control”. Then there are the non-Martys such as Catch Me If You Can, Inception, The Revenant and Once Upon a Time … in Hollywood. Judi Dench purred when she told me about the screen skills of DiCaprio and nobody else comes close to the claim of best American actor of his generation.

“I mean, it’s like explaining to somebody why you’ve fallen in love with them,” Anderson says, laughing dryly, when I ask what DiCaprio does differently. “But also, from time to time, I would be hit with a pang of jealousy. I’d think, ‘Quentin [Tarantino] has had his hands on him twice.’ But the idea had to come from me, I had to write something.”

One Battle After Another is meticulous — a labor of detail and love only possible when a studio takes a gamble. For one scene DiCaprio was in a supermarket full of real customers. “People were taking selfies — it was controlled chaos,” DiCaprio says. Anderson shrugs. “If a film crew lingers in a supermarket long enough, it doesn’t matter if Leo is there. They’ll just be, like, ‘F*** this, I’m here to do my shopping.’ They’ll get bored soon enough.”

One cinematic bomb he has made: DiCaprio in One Battle After Another.

“But it’s not often you get to be part of a process,” DiCaprio adds, meaning not only working with civilians, but, as Anderson does, showing his cast footage of what they have shot every day. “I remember very early on in my career getting VHS tapes in my trailer but, actually, this is something you never get to do.” He seems sweetly astounded. Maybe he could suggest it on his next film?

“‘You know, Marty, Paul did dailies,’” Anderson mocks, of his process of showing footage to actors. Of course DiCaprio’s next film is with Scorsese — a ghost story called What Happens at Night, which starts shooting this month.

DiCaprio and Anderson buzz about a particular scene shot in El Paso, Texas, in which on-the-run Bob needs help from a local activist and sensei (Benicio del Toro). Revolution is in the film and, indeed, in the air of El Paso, next to Mexico. “Our film has Immigration and Customs Enforcement-like officials [I.C.E.] coming to get my daughter and we are literally in a border town where the threat of all of that is bubbling,” DiCaprio says. “We needed extras to create a mob and go, ‘Viva la revolución!’ They all said, ‘Let’s go.’”

“We had a test screening on the day that I.C.E. arrived in LA,” Anderson says. “It was a peculiar feeling because you never know — if the world is on fire, do people really want to go see a movie about the world being on fire?” But how did he make something so resonant that took so many years to write? “Well, people being shitty to each other never goes out of style,” he says with a shrug.

It is a febrile time for Hollywood, when President Trump wades in to criticize perceived enemies and networks can face repercussions from the government too. Was there any fear in taking part in something that sticks pins into authoritarianism and lampoons the American right? “It never even occurred to me to not be part of the film because of its political undertones,” DiCaprio says. “And I don’t think there is any specific political agenda or ideology attached to it. We’ve had reactions from both the left and right, which, to me, says something. And anyway, at the end of the film, Bob is just a dad who’s there for his daughter.”

Anderson adds: “We just want to contribute something optimistic.”

I wonder if the director has read any of the criticisms of his film — complaints, for instance, about its hypersexualized depiction of black women, although the African-American Film Critics Association did name One Battle After Another the second best film of the year. “I tend to just listen to the overly enthusiastic reviews,” Anderson deadpans. “But if there are engaged conversations to be had with someone who has a problem with the film, I would love to have them. Let us have a cup of coffee. Just don’t shout it at me. Is that fair enough?”

DiCaprio stares into the middle distance. I mention his Titanic co-star Kate Winslet. “Are you going to ask why they both weren’t on that f***ing door?” Anderson says, meaning the raft in Titanic that saved Rose, but not Jack. “There was definitely room.”

Indeed — but actually I was going to say that Winslet told me she has “wet herself” in DiCaprio’s presence and one of her biggest secrets is that her old friend and co-star is funny. “A secret?” Anderson says, cackling. “He’s one of the funniest people I know.” DiCaprio grins. “I am taking my stab at comedic moments in my old age,” he says, with a slight smile, before standing up to leave — a man laser-focused on the movies, the great love of his life, and what might come next for them.

One Battle After Another is available on all major streaming platforms

Jonathan Dean is a senior writer at the Sunday Times Culture section and the author of I Must Belong Somewhere: Three Men. Two Migrations. One Endless Journey