On the day Daniel Brühl comes to London to meet the Guardian, Niki Lauda is in Germany at the Nürburgring racetrack. Lauda is there for the Grand Prix, in his capacity as non-executive chairman of the Mercedes Formula One team, although Nürburgring is also where, in 1976, the Austrian had the crash that almost killed him and left him disfigured. The accident is the epicentre of Ron Howard's Rush, which dramatises the rivalry between methodical champion Lauda (played by Brühl) and his womanising, booze-guzzling nemesis, Britain's James Hunt (Thor's Chris Hemsworth).

Brühl is stuck here talking to me about Lauda and the crash, while the real deal is over there where it all happened. "I know!" he says, springing forward. "Ron called me, super excited, because they organised a screening for the drivers and the actors and Niki at the Nürburgring, and the reactions were overwhelming. Lewis Hamilton, Alonso – everyone came over to Ron and there was a standing ovation. I was very sad to miss it. When he called me I said: 'What the fuck!' I wish I'd been there to see it with Niki, to watch him watch it, and see it with all those drivers."

Set in the 1970s, when Formula One was significantly more dangerous than it is today, Rush explores its racers' blind ambition, mythologising Lauda and Hunt as two sides of a coin: head versus heart. It's a big film, and a big deal for Brühl. Born in Barcelona to a German father and Spanish mother, he was raised in Cologne. His breakthrough came in 2003's Good Bye Lenin!, a touching Berlin Wall comedy. Inglourious Basterds, in which he played the lovelorn Nazi sniper, gave him blockbuster exposure. But Rush, an enthralling thrill of a ride in every sense, is his A-list graduation.

On screen, all traces of Brühl disappear – he looks like Lauda, sounds like Lauda, and projects Lauda's single-minded determination with a force that has the edge on Hemsworth's testosterone-fuelled Hunt. He gives nuance to Howard's broad strokes, conviction to Peter Morgan's brutally economic dialogue, and is so convincing in the role that I half-expect to meet Lauda himself. It's almost a disappointment to discover Brühl is a perky, giggly chap in a beanie hat and jeans. However, he litters his anecdotes with Lauda impersonations, uncannily channelling the driver as he does.

Lauda at Brands Hatch, a couple of week before his fateful crash in Germany. Photograph: Rainer W Schlegelmilch

Lauda is an icon in Germany and Brühl found the audition intimidating. "Normally they let you rot for two weeks then they call and say: 'You were awesome but it's not you,'" he says. "Three days after the audition I was on holiday in Spain with my girlfriend and I was overtaking a truck, and she was screaming at me: 'You are not a rally driver! You are not a good driver, stay behind the truck!' And at that moment I got the call saying it was me."

He had begun working on his accent when Lauda called. "The phone rang at 8am. I saw the number and thought: 'Oops, that's him.' He said: 'Yeah, it's Niki. I guess we have to meet.' I said: 'Yeah, it would be good.' He said: 'OK, come to Vienna. Just bring hand luggage so if we don't like each other you can piss off.' It was so brilliant. I thought: 'Oh my God, that's the way he is, OK.' So I packed my little bag and went to Vienna. Fortunately, he did like me and I had to buy some clothes because the trip was extended."

There he got an intense introduction to all things Lauda, who told him not to be afraid to ask about "the delicate subjects: the accident, the fear. Austrians are so easygoing. The first night, he was with his wife, and by coincidence [his ex-wife] Marlene was flying into Vienna. He said to me: 'Well, have dinner with us tonight, my new wife and my ex-wife, and you're gonna see it's more explosive than a Formula One race.' And it was just brilliant, seeing Niki there in the restaurant where he always sits, with all those friends of his, and then the ex-wife coming in, who told me lots of stuff about him from the past. I was constantly absorbing information."

Brühl admires Lauda's straightforwardness, both on and off the track. "He's very sharp and honest," he says. "He never repeats himself like I do. I'm a very redundant talker. Never would there be a word too much with him because that's a loss of time, a loss of money."

Hunt was Formula One's playboy and hedonism personified. But Lauda stopped at nothing to achieve success. Indeed, getting back behind the wheel mere weeks after a near-fatal crash is arguably more rock'n'roll than sex and drugs. Lauda was the reigning Formula One champion when, on lap two of 1976's German Grand Prix, his Ferrari slammed into an embankment and erupted into flames before being hit by another car. His helmet was thrown off and he was trapped in the burning car for 45 seconds before being freed. Toxic gas had damaged his lungs, part of his scalp had burned away, along with his eyelids and half an ear. In hospital, he fell into a coma and was read the last rites, but six weeks later he returned to the Grand Prix, refusing all cosmetic surgery other than the eyelid replacement which would enable him to see.

"In his autobiography, it's a short chapter," says Brühl, "because there's such a big hole. And talking to him, it's not that he wasn't willing to talk about it, but he's erased it. Maybe as self-defence he tried not to think too much about it, to look forward. That's why he was so emotionally moved when he saw the film. He told me he hadn't thought about it for such a long time and it was very weird to see himself again in that situation. It must be tough to see that."

Lauda says Rush made him realise how close he was to death. He was awed by Brühl's performance, and the actor, clearly very fond of him, would like to stay in touch. "I'm very tactile," says Brühl. "Maybe because I'm half-Spanish. I love to hug my friends, something that Niki doesn't like at all. So I immediately felt a certain distance because Niki is not a man who pretends to be friends after meeting someone a couple of times. He has a reputation for being cold and strict, but I had a perfect time with him, he supported me with everything I needed. People close to him said it was surprising how gentle and nice he was to me. I had the impression there was good chemistry between us, and there is."

Daniel Brühl with Benedict Cumberbatch in The Fifth Estate. Photograph: Frank Connor

Meanwhile, Brühl is forging ahead with a slew of big-hitters. Next month he co-stars with Benedict Cumberbatch in the WikiLeaks drama The Fifth Estate; Brühl plays Daniel Domscheit-Berg, Assange's former righthand man. "It's such a delicate subject, and when we were shooting we had to be careful and responsible," he says. "In the media Assange has said it's an anti-Assange, anti-WikiLeaks film, and it is not, it's clearly not. The villains in the movie are governments and armies and Swiss banks, not Assange." Early next year, he stars with Philip Seymour Hoffman and Willem Dafoe in Anton Corbijn's A Most Wanted Man.

His real love, though, is tapas. In Kreuzberg in Berlin, Brühl owns Bar Raval, a tapas bar named after the Barcelona quarter in which he spent his youth getting wasted (he always spent his summers in Spain, and now lives between there and Germany). "I'm pretty involved," he says. "The nicest part about it is to constantly be a spy and try different tapas in different cities, to see what we can improve. I take pictures and call my cook and tell them what they do. There's a good one here in Soho I have to try."

And off he goes, on the brink of global stardom, in search of new recipes.

Rush goes on general release in the UK on 13 September.