In the spring of 1924, Maurine Watkins, a young reporter for the Chicago Tribune, covered a murder trial in which a 24-year-old woman stood accused of shooting her lover. While Harry Kalstedt lay dying, prosecutors claimed, Beulah May Annan played jazz records and drank cocktails over his cooling body. Even after she was acquitted, the Tribune continued to refer to her as “Chicago’s Jazz Killer”.

That same month Belva Gaertner, a 40-year-old cabaret singer, was acquitted of killing her lover and told Watkins: “Gin and guns – either one is bad enough, but together they get you in a dickens of a mess, don’t they?” If it sounds a little too neat to be true, who cares? Two years later, Watkins wrote a stage play in which Belva became Velma, Beulah became Roxie and the basis for the longest-running American musical of all time was born.

Facebook Twitter Pinterest Cuba Gooding Jr as Billy Flynn in the forthcoming West End revival.

Chicago is still playing on Broadway and returns to London’s West End this spring, after a six-year hiatus, with Cuba Gooding Jr as Billy Flynn, the lawyer who defends both women. It brings with it that strange combination of the familiar and the modern. The fishnets, the backbends and the formation dancing are so engrained in our ideas of what showbiz is, they risk running into cliche or kitsch. And yet, when you revisit John Kander and Fred Ebb’s songs, you are reminded of how Chicago floats free from both its mid-1970s inception and its 1990s revival in a way that rescues it from nostalgia.

It probably helps that – unlike Liza Minnelli and Cabaret, another Kander and Ebb musical – Chicago is less emphatically associated with a single star or song. Bob Fosse, who co-wrote the book and choreographed, died in 1987, and Fred Ebb in 2004. But John Kander, at 90, continues to work – most recently, on an off-Broadway production of his new musical, The Beast in the Jungle. On the question of why Chicago is still popular four decades on, he is somewhat mystified.

“Really?” he says, over the phone from his apartment in Manhattan, when I mention that Chicago has now made over $1 billion worldwide. “I should get my windows cleaned! It sounds corny, but the excitement lies in doing it. Not that you don’t feel lucky if a piece works, or sad if it doesn’t, but I tend to move on. I think being allowed to make art and see it through to its completion is an extraordinary piece of luck.”

The luck was partly timing. Chicago was well received when it opened on Broadway in 1975, running for two years and a respectable 936 performances. But it was the 1996 revival that really caught fire. Its initial popularity may have had something to do with the fact that it opened in the aftermath of the OJ Simpson trial. “You just didn’t know if life was imitating art or art was imitating life,” says Ann Reinking, the dancer who played Roxie in 1977 and again during the revival, which she choreographed in Fosse’s style. “The message was potent right then.”

The message is that no corner of American life is exempt from corruption, and the satire is as subtle as a sledgehammer

Chicago’s message is broad – balanced on the homily that no corner of American life is exempt from corruption – and the satire is about as subtle as a sledgehammer. “Murder’s a form of entertainment,” says a character at one point. It can, at first, be hard to love. Like a lot of people, I came to the show via Rob Marshall’s 2002 movie, in which Catherine Zeta Jones plays Velma and Renée Zellweger is Roxie.

There is something almost amateurish about how nakedly Zeta Jones seems to identify with her character – I mean that in a good way – while Zellweger, the superior actor, plays her character as half winsome, half unhinged. The fact that neither sings particularly well is a limitation that, perversely, helps the film overcome its tendency towards tiresome slickness, as does John C Reilly as Amos, Roxie’s faithful but terminally dull husband – and the heart of the movie. Meanwhile, one has at least in theory to approve of Richard Gere, twinkling away as Billy Flynn.

Facebook Twitter Pinterest Renée Zellweger, Richard Gere and Catherine Zeta-Jones in the Oscar-winning 2002 film. Photograph: Circle/Sto/Rex/Shutterstock

Still, it struck me as overly stylised – easy to admire for its cleverness but difficult to warm to. Ben Brantley, reviewing the 1996 revival in the New York Times, said Fosse had given the 1975 cast this advice: “Dare the audience to look at you – and then look back at them with murder in your eyes.”

What wins one over in the end is the quality of the music and the way it speaks to Fosse’s choreography. Reinking, who now lives in Arizona and starred in the Fosse biopic All That Jazz, can remember exactly how she felt the first time she saw it. “I thought I was watching something brilliant, quietly strong. I couldn’t get it out of my mind. Mr Fosse was obviously influenced by Brecht and Weill, as well as Bergman and Fellini, and you could see the influence of vaudeville and African American hoofing – and Fred Astaire, too.”

If its naughtiness can sometimes seem dated, its underlying bones are still strong. “I don’t know if at any point in Chicago, anyone does anything you approve of,” says Kander. “Maybe Amos. After he’s sung his little song about nobody ever watching him, he says, ‘I hope I haven’t taken up too much of your time.’” What remains radical about Chicago’s amoralism, perhaps, is its ability to wrong-foot its audience, suckering them into sympathising with two murderers. There is no innocence to be squandered in the show, says Kander, because “everyone is rotten”. On his desk, he says, is a picture of Judi Dench as Sally Bowles in a 1968 production of Cabaret: Chicago implicates its audience in ways that built on that earlier musical.

He mentions the song in Cabaret called Tomorrow Belongs to Me, which opens with the lines: “The sun on the meadow is summery warm / The stag in the forest runs free / But gathered together to greet the storm / Tomorrow belongs to me.” Says Kander:“The feeling we were trying to create was, ‘Isn’t that lovely and wouldn’t you like to be part of that?’ Then, hopefully, when it’s repeated at the end of the second act” – as a Nazi anthem – “you know what it really means – and you’re not only horrified, but you’re complicit.”

Facebook Twitter Pinterest ‘It should always be sensual’ … Chita Rivera and Gwen Verdon in the first production in 1975. Photograph: AP

A similar dynamic is at play amid the snap and hustle of murderer’s row. This is something Kander and Ebb are very good at: using the audience’s weakness against them to underscore the themes of the piece. The musical’s target – the celebrification of American life – is broader than Cabaret’s. Although it is somehow a less personal musical, it reaches more deeply into American life in a way that can feel like the country turning around to talk to itself. As Kander says in his self-effacing way: “I’m afraid Chicago is timeless not because of any talent involved, but because of the subject.”

The danger, says Ann Reinking, was never that Chicago would be too cheesy, but that it would be too crass. “Every step is basically a word,” she says, “especially with musical theatre, because you’re not doing it for dance’s sake, you’re promoting a story – and, more than that, a moral. You’re propelling a story. So the steps – as well as the lyrics and the music – combine always to progress the story. They really are another form of language.”

The show, says Reinking, has to be careful in how it makes a political and moral statement. “It should always be sensual,” says Reinking, “but it should never get bawdy, unless you’re the most brilliant burlesque person in the world, where it’s so over the top you don’t care because it’s so funny. But it has to have a certain amount of taste. It needs to be elegant. And it’s definitely a paradox, but you work in the paradox. You don’t go overboard in one direction or the other.”

Facebook Twitter Pinterest ‘It has to be elegant’ … Ann Reinking, right, with Bebe Neuwirth in the 10th anniversary performance on Broadway. Photograph: Bryan Bedder/Getty Images

In other words, if the show has any shock factor at all, it should not be in the salaciousness of the dancing but in the force of its moral. “The odd thing about Bob,” says Reinking, “is that even though he’s known as really taking chances and being very sensual, he was also a very moral man.”

Kander looks in on the New York production occasionally and says they keep it “in pretty good shape”. Why hasn’t it dated? “I think about that,” he says. “And I start to wonder why. And of course I know why – because corruption in society never seems to go out of style. Every once in a while, it becomes more obvious than not. And – God – just when I thought ‘Is Chicago still going to be pertinent?’, we have our lovely president and everything that comes with him. All of a sudden, it feels brand new again. Isn’t that awful?” He sounds delighted.