Robert De Niro, 65 and still passable in his underpants — more of them later — is smiling at me in exaggerated bemusement, the kind of look he gives people on screen before he kisses them on both cheeks or shoots them. I’m asking him about Johnny Boy in Mean Streets and the moment he starts dancing while Harvey Keitel’s Charlie waits in the car for their getaway. This was the moment when I knew that no matter how repulsive the actor’s future creations, the upstart villains, stalkers and brutal assassins, there would also be a reason to like or pity them. Who told him to dance?

“Oh, I don’t know,” he laughs. “It’s too long ago.” But I’m not having that — not when we mostly agree the greatest lines of contemporary cinema are built on this man’s improvisations.

The hat that told you more about madcap Johnny — his swagger, his self-importance, his danger — than any close-up wasn’t from the wardrobe department, but from the collection of clothes and accessories the young actor kept at home in Greenwich Village.

And it was his inspired free-form three years later in Taxi Driver that made the movie a classic. The only direction for Travis Bickle’s famous “Are you talkin’ to me?” sequence as he practises for the assassination of the presidential candidate was a simple “He looks in the mirror”.

When Martin Scorsese wants a reality check on set, he asks the actor a simple question “Does it feel right?” Thirty-five years later, De Niro is still doing more feeling than talking, but he seems more benign than his volatile reputation allows. Maybe he’s realised he’s in the room with a fan (but frankly, how could he ever not be?), and that if I’m intending to ask him why he has done so many mundane pay-cheque movies in the past 15 years, I’m leaving it to the bitter end.

At a later point in the proceedings, Art Linson, the producer and his buddy of more than 20 years, leans forward and tells me, not unkindly, “You are just like everyone else,” meaning that

I am letting my regard for the genius cloud my appreciation of how normal in its stresses and strains his life really is. De Niro listens to the assessment neutrally; I doubt if “normal” was ever quite the word for him. On a trip to Cannes earlier this year, where their new movie What Just Happened closed the festival, the star alighted from his car to a bizarre chorus of “Bobby, Bobby, you talking to me?” in thick French accents. He shrugs and offers that enigmatic little smile; he was flattered — the movie was born before most of the fans.

In his new bitter comedy of morals he plays Ben, an embattled Hollywood producer, buffeted by the egos and tantrums of spoilt actors and fearsome studio executives, a character whose stress levels start off making you laugh (“Cigarette? Why not? It’s only been 30 years”) and end up making you feel queasy. As he sits in the screening room watching the gruesome and uncommercial finale of a picture on which his career rests, his face does nothing — and everything. Without moving a muscle, De Niro conveys Ben’s utter horror in knowing he is about to be eviscerated by the money men.

“It’s funny,” he muses, “actors have a tendency to want to express something when there’s a big moment, but in life, when there’s an extremely traumatic moment, often nothing is done. Absolutely nothing. Only the face and maybe the eyebrows move, no comment, no spin. Look at a person who has just been told their two children have been killed in an automobile accident, and they just look. They do nothing. It’s just shock.”

On a rainy Monday afternoon on Park Lane the icon seems relaxed. Maybe because he is happy about the coming of Obama, for whom he campaigned with the other lib-celebs, his hopes pinned not on tax breaks for movie-makers but on new foreign policy.

“It would have been a disaster for our country, and the world, if it had gone the other way. Period. Thank God.” He glances over at Linson, with whom he saw the election results come in. “He cried,” snorts De Niro, teasing his pal.

“It was ridiculous. He cried.”

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