Beautiful Boy is based on a brace of memoirs that together provide a father-and-son, “he said, he said” account of the same story. The books in question are Tweak: Growing Up On Methamphetamines by Nic Sheff, and Beautiful Boy: A Father’s Journey Through His Son’s Addiction by Nic’s journalist father, David. Timothée Chalamet – currently Hollywood’s hottest young actor after his Oscar nomination for Call Me By Your Name and love interest in the also Oscar-nominated Lady Bird – plays the teenager hooked on crystal meth. Steve Carell is the father trying to understand what has happened to his apparently perfect, happy-go-lucky son. The film displays an unusual commitment to the cyclical nature of addiction, where promises are followed by relapses and feelings of shame followed by yet more promises. It is essentially a two-hander, so it seems only right that the actors should be performing promotional duties together.

Carell, 56, is the first to arrive in our London hotel room. He is wearing a dark brown suit, white shirt and tie, and is unfailingly genial. While we are waiting for Chalamet to arrive, I produce from my bag a book that I happen to be reading: Improv Nation, Sam Wasson’s history of American improvisational comedy, which includes material about Second City, the Chicago-based troupe in which the likes of Carell, Tina Fey and Stephen Colbert cut their teeth. I flick to the page showing Carell, Colbert and two other comics dressed as the Beatles. It is a photograph he hasn’t seen for many years and he looks genuinely gobsmacked. “Oh wow. This is incredible.”

At that moment, the 22-year-old Chalamet comes bounding into the room. Bright-eyed and milk-faced, he is in pinstriped trousers and blindingly white trainers; on his green socks are tiny yellow lightning bolts. “Timmy, come see this,” says Carell, holding the book open at the photograph of the four baby-faced young men in mop-tops and collarless suits. “Here’s me. And that’s Colbert.” Chalamet, who can’t say “um” or “er” without making it sound emphatic, hoots with joy. “Oh my gosh!” he cries.

It is a flashback to a different Carell, the exclusively comedic one familiar from The Daily Show, Bruce Almighty and Anchorman: The Legend of Ron Burgundy, long before Little Miss Sunshine proved there was more to him than goofing around. It is hardly noteworthy these days when he takes on a straight part such as Beautiful Boy. But it is hard to overstate the glorious surprise of his performance in Foxcatcher as the sinister billionaire John du Pont, whose ambition to coach the US Olympic wrestling team is driven by patriotism and latent homosexuality. “It was a surprise to me, too,” he says. “I didn’t think I’d get that call. It didn’t seem that was going to be my trajectory. Though I have to tell you, when I read the script, I did think I could do it. I was afraid of it, but I think that having a little fear is a good thing. That means there’s a challenge at hand and something to dig into.”

We meet in October and it already seems clear that the awards prospects for Beautiful Boy begin and end with Chalamet. Carell’s own chances lie more with his portrayal of Donald Rumsfeld in the political comedy Vice, opposite Christian Bale as Dick Cheney. He will also be seen in Welcome to Marwen as an artist who deals with a violent attack by creating a miniature world populated by action figures to process his trauma. (“From the director of Forrest Gump,” proclaims the poster – and it shows.)

Chalamet as Nic Sheff and Carell as David Scheff in Beautiful Boy. Photograph: François Duhamel/StudioCanal

Nic is the jazzier part, the one full of vertiginous highs and gutter-licking lows, though anyone who has read Tweak may wonder where the grittier specifics have gone. That moment when Nic believes himself to be a spider, for instance, or his experience of selling his body for drugs. Why aren’t they in the film? “For me, it goes back to meeting Nic and David,” explains Chalamet, “and getting the sense this wasn’t a biopic, and that just making it human was the most galvanising, uh, imperative. I realised I should lean away from playing a drug addict and rather play a human who’s in a very difficult set of circumstances.” Does that explain why Nic’s candour about the joys of crystal meth (“There was a feeling like – my God, this is what I’ve been missing my entire life. It completed me. I felt whole …”) is absent from the movie, too? “I think that quote is really just a lens into him diving into it but he never points to the why and nor is it about the how. It’s more about how to go forward and how to overcome, I think. And secondly …” He stops and laughs. “Oh, I guess maybe that’s all I was gonna say.”

Chalamet’s performance has best supporting actor stamped all over it. Indeed, that is the only Golden Globes category in which Beautiful Boy has been recognised. But Carell’s task is arguably the trickier one. He has to play caution and uncertainty: far less dramatic colours on an actor’s palette. At one point, Nic complains that David is too controlling, and the film hints at how suffocating this father’s love must be, how inhibiting his admiration. Did Carell sympathise with Nic’s objections? “Oh, even in a drug-addled state I think Nic makes a lot of salient points,” he says. “And yes, I think some of them hit home. David realised, certainly in retrospect, that he had made mistakes and been controlling and ego-driven. Nic says: ‘I was this amazing thing, this special creation, and you don’t like who I am now.’ He’s no longer this representation of what he wants in a son. All that is true and that strikes David because he’s being self-centred about Nic’s addiction in lots of ways, looking to himself for what went wrong. It’s one of the stages he goes through in figuring out it’s not about him at all, or what kind of father he was. It goes deeper than that.”

Delve into the reasons for addiction, though, and both actors recoil. “People can extrapolate what they will when they watch it,” says Carell. “I certainly can’t speak to why Nic became an addict or what triggered him.” Chalamet, too, scrupulously avoids straying into the subjective. He answers my question about whether the film might send panicky parents into a Reefer Madness-style paranoia by saying: “I think that’s fair, well, I don’t know if it’s fair but I think people are entitled to their own reaction.” Elsewhere he is careful to pepper his conversation with qualifying phrases: “I may be wrong” and “I’ll try my best to answer that”. When I mention that David, in his book, confessed that his son’s woes had made it impossible for him to see addiction in anything but a solemn light, and that he couldn’t even laugh at a film such as Sideways, Chalamet cuts me off politely. “I haven’t seen Sideways,” he says.

Fair enough. But what about drug humour: Dazed and Confused, Cheech and Chong? Will you still be able to enjoy those now you’ve made Beautiful Boy? His answer is a circuitous one. “It’s tough ’cos I’m young and, and I love pop culture and certainly what I say next, I’m not an authority on in any way, and I don’t want to be cavalier about it, and I don’t have a solution to it, but just to observe it as a phenomenon – there’s a scene in Beautiful Boy that references Nirvana and there is equally a nihilisation of, um, not even necessarily to addiction, I’m not even saying it’s, you know, there’s um … particularly now it’s like a longer conversation or something, but like with SoundCloud rap, that’s a good example.” I look at Carell, who gives a faint “search me” expression, so I explain to Chalamet that I’m middle-aged and what’s SoundCloud rap please? “It’s a real lens into a lot of the disillusionment young people feel, not only in America but all over the world, and how they’re dealing with it by numbing, with opiates and Xanax, and there’s a glorification of it that I would encourage you to see that I’m not saying anything about but I’m just saying it’s there and, um, equally it felt like there was integrity to this story because it’s really, like, an anti-glorification.”

A scene from Beautiful Boy. Photograph: StudioCanal

This is the difficulty experienced by actors promoting serious-minded material. In a recent article for Deadline, the veteran industry insider Peter Bart wrote about the special twitchiness of publicists who know that a single mis-spoken comment can derail an awards campaign: “The ubiquitous Q&A sessions pose a special problem in that no one knows what questions to expect … Given the formidable list of addiction dramas this year (involving everyone from Bradley Cooper [in A Star Is Born] to Lucas Hedges [in Ben Is Back] to Timothée Chalamet), actors are warned to avoid references either endorsing or denigrating drug use – even weed or aspirin.” Say the wrong thing, or even an ambiguous thing that could be misinterpreted, and it’s goodbye, Oscar.

We have five minutes left, and the subject of drugs has been a slightly fraught one, so I invite them both to tell me what they have each admired about the other’s work. Carell mentions his co-star’s performance as the cooler-than-thou guitarist in Lady Bird. “I said to my wife afterwards: ‘That one guy. Who is that? What’s going on? There’s something special there.’ To see him first-hand and watch how he works, to act beside him, was a real joy. So in fact I think his performance in Beautiful Boy is my favourite on a selfish and personal level because I witnessed and shared in it.”

Chalamet throws up his hands when it’s his turn to answer. “There’s so much! Foxcatcher, Foxcatcher, Foxcatcher. The Big Short. Bruce Almighty, which I saw with my family in the theatre when I was eight. And it’s funny, Steve said to me recently that he thought he was going to be cut out of that film.” I look at Carell, who nods sadly. “Or The Office,” Chalamet continues. “I had my soccer beanbag chair in my room with my Xbox 360 that I could stream Netflix on before it was readily streamable, and my Dad and I went through all the seasons of The Office before Steve left the show.”

The pair have a couple of things in common. They were both nominated for best actor Oscars (Carell for Foxcatcher, Chalamet for Call Me By Your Name) and both were unfairly beaten by British actors (Carell by Eddie Redmayne in The Theory of Everything, Chalamet by Gary Oldman in Darkest Hour). “Thanks for bringing that up!” splutters Carell. Wait, I protest, I said “unfairly beaten”. But he isn’t placated. “No, no,” he laughs. “Thanks for just throwing that in our faces.” And they have both, of course, worked with Woody Allen: Carell twice, on Melinda and Melinda and Cafe Society, and Chalamet on A Rainy Day in New York, which may never be seen now that Allen’s past has been lumped in with the #MeToo revolution. I start to ask them both what they learned from working with this great director but it’s too late. The mere mention of the name “Woody Allen” translates in the ears of the nearby publicist into the words: “Please curtail this interview now.” And she does. Oh well. You can’t be too careful when there are Oscars at stake.

• Beautiful Boy is released 18 January.