The idea of remaking the series as a film seemed to make commercial sense, especially after the enormous success of The Godfather and its sequel. Its studio Paramount turned to the producer Art Linson, who was responsible for successful comedies such as Car Wash and Fast Times at Ridgemont High, and asked him whether he would be able to put together a similarly high-class package.

The offer left Linson with mixed feelings. He had never been an especially big fan of the original television series, but as he wrote in his memoir A Pound of Flesh: “I loved the subject matter... Al Capone, Eliot Ness, bootlegging, machine-gun violence and Chicago in the 1930s were a significant part of American folklore.” If he could attract the right filmmakers, it could have great potential. As he said: “I wanted a high-priced writer who would distinguish the movie, rather than approach it as another trashy remake chasing a famous title.”

Enter Mamet, who was not only a Chicago native, but a Pulitzer Prize winner for his play Glengarry Glen Ross. He had attracted plaudits for his screenplay for The Verdict, but that was a far more serious film. The Untouchables was intended to be a big summer blockbuster. If Mamet could be seduced, then the film could work. If not, it was barely worth making.

Linson’s first impression of the playwright was that “he reminded me of a Jew with a buzz cut trying to impersonate a biker”, and he liked him enormously. Mamet was less excited, and regarded the producer with a mixture of suspicion and distrust. Linson suggested that “I must have reminded him of a clammy rag salesman in casual clothes.” They met for lunch in SoHo in New York.

Linson had intended to offer Mamet a long and detailed pitch about the cultural and historical significance of the project, and why it would be of a piece with his career as a dramatist. It therefore came almost as a surprise to him that he instead blurted out: “Dave, don’t you think that the best career move for somebody who just won the Pulitzer Prize would be to adapt an old television series like The Untouchables for a s___load of money?”

Mamet, without missing a beat, agreed, and delivered his first draft within four weeks. Linson, who was used to writers taking up to a year, was impressed by what he read. Although the Capone character was thinly drawn, he could see that Jim Malone, in particular, would attract a major star, and described the screenplay as “emotional, witty and filled with unexpected, memorable exchanges that would distinguish it from the television series”.

But there were immediate difficulties. Mamet was unreceptive to rewrites and refused to spend more than a couple of days on them, and, after A-list directors turned down the screenplay, there was increasing unease at the studio about the project. As Linson said tactfully: “The first thing you notice about a Mamet script is that the characters do not always sound conversational in the way we are used to.”

The studio’s first reaction was to fire Mamet and hire a more conventional, pliable screenwriter, and when Linson dared to suggest to the playwright that he should be more responsive to executive notes, Mamet calmly said: “I weigh them before I throw them away.” If an A-list director could not be recruited, then, as Linson said: “The new version of The Untouchables would be headed toward the warmth and comfort of familiar mediocrity... written by committee and certainly without Mamet.”

Yet when the producer had a meeting with the “large, abrupt and seemingly stern” de Palma, who had expressed interest in directing, he was faced with another kind of difficulty. As he said: “You are instantly given the feeling that if he hasn’t yet scared the s___ out of you, he eventually will.” The legendary director of Scarface, Dressed to Kill and Carrie was not an easy or congenial man. Linson was explicitly warned that “with the two of us in the same cage, I would last for about a week.” De Palma needed a hit after two back-to-back flops in the form of Wise Guys and Body Double, so he committed to the project, but with reservations. “We have a lot of work to do,” he said. “This script needs to be addressed, and this picture is going to cost more than they think it is.”

Casting was a major issue. De Palma met with Kevin Costner for the central role of Ness; he was not especially interested in the part, and the actor was also an unknown quantity at the box office, having never carried a film of this kind before. But de Palma and Costner hit it off and, after failed attempts to interest Mel Gibson and Don Johnson in the role of Ness, the actor was hired and attention turned to the big-name stars who had to be cast in the roles of Malone and Capone.

De Palma stated from the outset: “We’ve got to get a movie star like Sean Connery to play Malone... if I kill [him] off in a movie, no one will believe it.” Like his idol Alfred Hitchcock, De Palma was notorious for killing off his leading actors in unexpected fashions – Angie Dickinson, the supposed star of 1980’s Dressed to Kill, is brutally murdered after 20 minutes – and Connery agreed to take on the role after meeting with Mamet and de Palma. His usual fee was $2 million, which would have wreaked budgetary havoc, but his canny agent Mike Ovitz negotiated another deal; Connery would take no upfront fee in exchange for a percentage of the gross if the film was a hit. He ended up making considerably more.

The casting of Capone was more difficult. It was felt that the character, who only appeared in three scenes in the original script, should be an outsized, almost grotesque presence; John Candy was at one point suggested in an example of casting against type. But it was instead felt that the British actor Bob Hoskins, who had brilliantly combined charm with menace in the gangster films Mona Lisa and The Long Good Friday, would do a better job, and so he was hired for a fee of $200,000.

Then de Palma casually mentioned that his friend and former collaborator Robert de Niro was interested in playing Capone. Not only would casting the most sought-after and acclaimed actor of his generation in the role give the project unimaginable kudos, but the presence of the man who played the young Vito Corleone in a pivotal role of this sort would be totemic.

Yet the budget was clambering higher and higher, and de Niro’s fee would run into the millions. Paramount were horrified, telling Linson that “we are not spending $20 million to remake a gangster movie…tell your director that he better start looking at himself in the mirror and coming up with the right answers.” A compromise was reached. Capone’s scenes were scheduled for the end of filming, and Hoskins was still available; as Linson said: “He was not as electrifying a choice, but he was the only choice.”

De Palma, meanwhile, began to conceive of operatic set-pieces that made his paymasters sweat with terror. A full-on Western shoot-out on the Canadian border, complete with cavalry charge; deeply expensive recreations of Thirties Chicago; a climatic gun battle at Union Station that De Palma saw as an opportunity to pay homage to Eisenstein’s Battleship Potemkin. All of these would be hugely, ludicrously expensive. A reckoning was inevitable.

Paramount executive Ned Tanen called a meeting with Linson and de Palma shortly before filming was about to begin, in an attempt to keep costs down. The budget had been set at a maximum of $18 million, and the idea of its spiralling up to $20 million made the studio nervous. De Palma calmly outlined what he required; he wanted to hire De Niro as Capone, to indulge his penchant for epic and unforgettable action scenes and to make a modern-day gangster classic.

As he said: “If we stay with the cast we have, shorten the schedule and reduce the scale of the picture, [we] will end up with a movie that at best will be suited to ‘Masterpiece Theatre’. It is not the movie I want to direct. It will not work, and I cannot afford to make a movie that will not work.” Then he suggested what awaited instead. “When Bob De Niro kills somebody with a baseball bat, with me directing, it will never be forgotten.” Tanen was persuaded. A $22.5 million budget was agreed upon, and Hoskins was paid off, leading the actor to call de Palma and jokingly ask if there were any other films that he didn’t want him to star in.

Yet the casting of De Niro could have caused more trouble than benefit. Although the actor was only required for two weeks of filming, his obsessive attention to detail made his presence known far earlier. He refused to wear the (Giorgio Armani-designed) costumes, and instead demanded that his wardrobe as Capone be redesigned by Italian tailors, under his personal supervision; he even insisted on wearing a $3,000 suit that had been tailored by someone who had fitted Capone’s outfits. He gained 25 pounds for the role, and shaved his hairline so that his face looked wider and fatter.

He was even reputed to have worn silk underwear to understand the arrogance and entitlement of the crime lord that he was playing. It seemed a piece of extraordinary method-heavy self-indulgence, but it worked electrifyingly. As Linson said: “Without uttering a word, by merely strolling to his position in front of the camera, Capone-De Niro suddenly became sly, dangerous, confident and even witty.” The gamble had paid off spectacularly.