Jack and Marty. It seems inconceivable that probably the greatest American actor and director of the past half-century have not worked together before. Yet The Departed, a brutal crime drama set in Boston, is the first collaboration between Jack Nicholson and Martin Scorsese. The film, a loose remake of the 2002 Hong Kong movie Infernal Affairs, also stars Leonardo DiCaprio and Matt Damon.

“We’ve talked about working together many times,” Nicholson explains, “but you don’t always get to work with the people you want to work with.”

In fact, Nicholson, who is now 69, turned down Scorsese, 63, when he first called him to suggest playing the part of the Boston mob boss Frank Costello. Nicholson didn’t feel there was enough meat in the character as written. There was also the problem of Nicholson’s salary demands on a film that already had a lot of high-priced talent.

“You can always do it if you do it for nothing,” says Nicholson, in that unmistakable gravelly New Jersey drawl, pausing a beat for effect as he raises an eyebrow. “But I’m not into that.” Nicholson’s famously hard-driving deal-making has made him one of the richest actors in Hollywood: he earned more than $60m for just one part, the Joker in Batman.

Scorsese was so keen to snare Nicholson that he allowed him, as Nicholson says, “an unusual amount of involvement in re-conceiving the character”, including encouraging him to improvise a lot during shooting. Nicholson wanted to make Costello more evil than originally written, and he wanted to explore the sexuality of a powerful evil man. Scenes were shot involving Nicholson’s character, dildos, cocaine and prostitutes — not all of which made it into the version of the film I was shown, although I did get to see him produce a huge dildo from under his coat at a surprising moment. The dildos and cocaine were Nicholson’s idea, apparently.

However many sex toys made it into the final cut, Nicholson says he enjoyed working with Scorsese because “he really explores a movie; he doesn’t preconceive it that much”.

“And we have a similar background; we understand the Corman system” — an allusion to the renowned B-movie producer Roger Corman, for whom Nicholson and Scorsese both worked early in their careers — “that it’s not necessarily about ‘good’, but ‘now!’. Of course, we’re not totally under that system, but we had a very easy shorthand, and I think what we hoped and guessed about one another came true.”

One of the reasons Nicholson’s career has been so enduring is that his apprenticeship in the 1950s and 1960s, with Corman and at B-movie studio AIP, was as much as a writer and producer as an actor. He learnt, as he once said, that “a good actor can always be interesting, but fine acting involves the whole piece”. After more than a decade scraping by in mostly forgettable exploitation movies such as Back Door to Hell, Flight to Fury and Hell’s Angels on Wheels, Nicholson was seriously thinking of giving up acting to concentrate on directing. Then, in 1969, came his performance as the hard-drinking Southern lawyer in Easy Rider.

Overnight, Nicholson became the Jack we now know. With the astonishing run of seminal films that followed — Five Easy Pieces, Carnal Knowledge, The Last Detail, Chinatown, One Flew Over the Cuckoo’s Nest, The Postman Always Rings Twice, Reds, Terms of Endearment, Prizzi’s Honor, Heartburn, The Witches of Eastwick, Broadcast News — Nicholson became the indispensable, iconic American actor of his generation. Since the 1990s, when some people felt he had passed the zenith of his career, he has reinvented himself, in films like As Good as It Gets, About Schmidt and Something’s Gotta Give, as one of the few older Hollywood actors who seems to relish playing his age. He’s won more Academy Award nominations than any male actor in history: eight for best actor (of which he won two) and four for best supporting actor (winning once). Of course, his often racy private life has also kept him in the headlines: his friendships with people such as Roman Polanski, who directed him in Chinatown, and his relationships with Anjelica Huston, Rebecca Broussard and, more recently, Lara Flynn Boyle.

As much as Nicholson has managed to stay relevant to new generation of film-goers, there’s very much the air of an old- fashioned movie star about him. He talks a lot about “class”, which he feels is missing from the movie business these days. And he’s not keen on the aggravating business of publicising movies, preferring to avoid days of press junkets. He pulled out of a planned press conference in New York for The Departed at the last minute. I feel lucky to be given any kind of interview, ushered one recent afternoon into a smoky Beverly Hills hotel room for a brief audience.

Nicholson, in a blue striped seersucker jacket, bright-yellow sports shirt and beige trousers, his trademark shades on the table beside him, spends much more of my time slot talking about one of his pet peeves, the ineffectiveness of traffic lights, than about his role as Frank Costello in The Departed. Which I now think was probably intentional.

“I’m for none of this backstage revealing,” Nicholson explains at one point. “I know the value of mystery in the theatrical experience.” It’s true. As much as he has chosen to reveal to us in so many of the great movie performances of the last half century, Jack Nicholson remains an enigma.

The Departed opens on Friday