Shall we rerun those stats one more time? Eighteen separate productions. Currently up and running in 10 countries. Seen in endless others by, at the most recent head count, 30m people. Mamma Mia!, the show fashioned from the Abba songbook, is the only mega-musical to have proved itself unstoppable without any assistance from anyone called Lloyd Webber or Mackintosh, or any affiliation with Disney. Or, indeed, without any help from men at all (unless you thank Björn and Benny for the music).

Since 1999, when the show opened in London, the three queens of Mamma Mia! - the producer, Judy Craymer, the director, Phyllida Lloyd, and the book writer, Catherine Johnson – have been dancing all the way to the bank. The time was inevitably going to come when the people behind the stage show might seek to replicate their triumph on celluloid. So, as of next month, it’s the movie Mamma Mia! - here they go again.

Not that there’s any guarantee of more ringing tills, despite an all-singing, all-dancing cast led by Meryl Streep. She plays Donna Sheridan, the matriarch whose daughter, Sophie (Amanda Seyfried from Mean Girls), is the product of a jolly summer spent with a trio of men back in the fag end of the 1970s on the Greek island where she now runs a hotel. In the film, the three potential fathers, furtively invited by Sophie to her wedding, assume the rugged forms of Pierce Brosnan, Colin Firth and Stellan Skarsgard. Meanwhile, Donna’s two old muckers from her superannuated girlband, Donna and the Dynamos, are in the safe hands of Julie Walters and Christine Baranski. Also awash with attractive young things, mostly wearing their bathers, the cast seems designed to tick every imaginable box.

“A film can go anywhere,” insists Björn Ulvaeus from his home in Sweden. “Some famous film critic said, ‘The only thing we know is we know nothing.’ We haven’t a clue.” Chief among the clueless, at least before they started, were the show’s creative triumvirate, none of whom had ever made a film. In the late 1980s, Craymer, who met Ulvaeus and Benny Andersson when she was working for Tim Rice on Chess, toyed with a film suggested by the Abba songbook. “I didn’t dare propose a stage musical,” she says, “because I had left that world and moved into television and film. That was the safe bet for me.” Mamma Mia!’s eventual niche granted access to a demographic of fortysomethings who are still spending their money, money, money, but whether a younger mass audience will be seduced by, in Craymer’s image, “Meryl getting smoochie with Pierce and vice versa”, remains to be seen. And yes, there were Oscars galore for Chicago, but audiences smelt a rat when The Producers and Hairspray hobbled from White Way to silver screen.

“I think everybody was concerned, as always in the theatre community, that a movie might distract from the fact that there are live performances going on all over the world,” Andersson says. Well, they needn’t worry on that count. Mamma Mia! is now a global brand, with Craymer not so much producer as CEO. “It’ll go around the world for many years now,” Ulvaeus says. Next stop for the stage show is a cross-border raid on Oslo. There is talk of going back into China, not in English, as on a stopover last summer, but in Mandarin or Cantonese. Besides, a film might pep things up at the theatre box office. “Which actually happened with The Phantom of the Opera in New York,” Andersson says. “It was struggling for a bit. I don’t know if the movie did any good, but it definitely helped audiences to find their way back to the theatre.” So, this is by no means the end of the road for the show. “Only 30m people have seen it so far,” Lloyd says breezily, “so I hope not.”

The film was first mooted when Tom Hanks’s production company contacted Craymer’s early in the Broadway run. Hanks takes a credit as executive producer under the umbrella of Universal. The rights themselves were not, however, sold to Hollywood. “We wanted to maintain control,” Craymer says. Her endorsement did not stop Johnson from imagining that, like most scriptwriters, she would be chewed up and spat out by the machine. “I kept expecting I would be kicked off,” she recalls, “but I somehow managed to hang on in there.”

Having woven the songs into a narrative once, Johnson quixotically decided she had to prove herself all over again. “The first thing I did,” she says, “was try to rewrite the whole thing, throwing everything out. It was a challenge. I thought, ‘It’s time to reinvent Mamma Mia!’ - but I discovered that there is a structure you can’t tamper with.

There is a reason why the songs are where they are. Given that it took me 2½ years to get there in the first place, it was a bit insane to try to do it all again.” So, with various tweaks, the songs are back where they started, in the mouths of the same characters: Donna sings, among others, the title tune and The Winner Takes It All, shares Dancing Queen and Super Trouper with her chums, Rosie (Take a Chance on Me) and Tanya (Does Your Mother Know?), who have come over for the wedding of Sophie, who sings Honey Honey, and so on and so forth.

While Thank You for the Music has been hoicked out of the main body of the story and replanted in the closing credits, only two songs have been dropped altogether: Under Attack, which opens Act II in the stage show and surely won’t be missed, and Knowing Me, Knowing You, sung on stage by Brosnan’s character, Sam Carmichael, to Sophie, but now replaced by the less familiar When All Is Said and Done. “We just felt Knowing Me, Knowing You didn’t quite work,” Ulvaeus says. “On film, we didn’t need it to explain the things that we needed on stage.”

Johnson’s main difficulty came when the Americans insisted on their own patois for mother and daughter. A Bristolian whose potty-mouthed plays are incontestably English in flavour, Johnson gritted her teeth and typed out the word “Mom”. “I found it much simpler to write Julie Walters’s dialogue,” she says. “Even then, you’re having to fight for that. ‘Her character’s British. Why should she speak like an American?’” She did manage to smuggle one filthy little reference to water sports past Universal’s uncomprehending moral gatekeepers. (“Phyllida knows. I’m not sure Judy does. But if the film’s locked off, there’s nothing they can do about it.”) Craymer also fought to retain her director. “I’m sure Phyllida would have stepped aside gracefully if it had gone to some Alist director, but it was important to keep

everybody together.” Lloyd’s immersion in Abba’s world has always been a source of puzzlement – not least to herself, with her background in directing subsidised theatre and opera, including a recent Ring cycle for English National Opera. “Twelve years ago, if someone had said, ‘You will direct a West End musical,’ I would have fallen off my chair,” she says. “And to direct a Hollywood movie is similarly baffling. It was a little like opening a theatre show every day for 80 days.” Yet Lloyd chooses to see no directorial discrepancy between staging The Ride of the Valkyries in the Coliseum and shooting Voulez-Vous? in Pinewood. “The Ring and Mamma Mia! are both stories about lost parents,” she asserts, “and I approached them in entirely the same manner. My task was to let Mamma Mia! out of its cage and give it flight, and to guard its rough-and-tumble inner life vigilantly. That process was, I hope, achieved through the casting.”

Streep, who still seems to be hyper-ventilating about her involvement, first became aware of the musical when she took a party of 10 10-year-olds to the show when it opened in New York, soon after 9/11. Intoxicated by the sweet scent of escapism, she wrote a fan letter to the cast and creative team, copies of which, Lloyd reveals, “we have all had pinned to our fridges for years”. Several years later, the creative team got in touch. “My agent said, ‘You probably don’t want to’,” Streep recalls. “I said, ‘They want me?’ ‘Well, I don’t know if they want you, but they want to meet you.’ I said, ‘Oh my God, oh my God. Please, please, please.’”

It is Streep who puts her finger on the potential appeal of the film to cinemagoers, in a summer over which CGI has a virtual monopoly. It’s a chick movie in which Mr Bond, Mr Darcy and a token Swede play middle-aged totty. “Basically, what they play in this movie is the girls, the parts we normally play. There are the protagonists, and the men play the love interest. Stellan Skarsgard as eye candy: it’s a hilarious concept.”

Streep’s enlistment was enough to overcome, as the actor himself admits, the pig ignorance of Brosnan, who accepted the part of one of the three potential dads despite having no previous interest in Abba or knowledge of the show. “When the gig came in, they said, ‘Meryl Streep, Greece’ – ‘I’m in.’ I didn’t have a clue what the show was about. The blonde I fancied a lot as a young lad at drama school. She was a cracking-looking girl. And the rest was this frothy camp. It wasn’t me. But,” he allows, “I got the humour of me being in this.”

The penny didn’t drop that quickly. He had already signed up when he took his mother and children along to the London production. “And I realised I didn’t know who I was playing. Fifteen minutes into the show, I’m going, ‘Jesus Christ, Meryl has said yes...’ Then the heart relaxed. And when they come on to do Waterloo, you’re up, you’re standing.”

The show has always had that emollient effect on recalcitrant heterosexual males. The songbook lends itself perfectly to what, in America, they call “the jukebox musical” because, thanks to the band’s two marriages and two divorces, there are enough tunes about real heartache to counter the leavening impact of all that spandex. “The songs are in two categories,” Andersson concedes. “The first years, with the pop tunes, with pop lyrics that go in one ear and out the other. Once Björn got his hand on the writing pen, little stories, little slices of life, came into the songs.”

“Phyllida and Catherine tell me this is why it works,” Ulvaeus says. “The reason is that we tried to model ourselves on the Beatles, in so much as we wanted each album to be a step forward. I was always trying to find a new aspect of relationships. I don’t think many pop lyricists in those days thought the way I did.”

However musically accomplished and emotionally wide-ranging the songbook, audiences will be curious to know if they will need to block their ears before they follow favourite actors into the multiplex. Andersson spent a lot of time in his Stockholm studio with an orchestra and the Swedish cast of the show, working on rich underscoring that gives the cast maximum protection. With Streep, at least, nobody need have any fears. A mighty chest voice was unveiled in Postcards from the Edge, and, more recently, when she played a singer in an all-female act in Robert Altman’s A Prairie Home Companion.

“When I was young, I didn’t want to be an actress,” she says. “I wanted to be a singer. My mother took me to all these musicals and that was my love. When I went to university, I thought I’d be a music major. Then music theory happened. So I just got involved with the drama department.

“The mountain in the score is The Winner Takes It All. But it ended up being not that hard, in fact. It’s so thoroughly imagined an emotional journey. For an actor, it’s hard when the writing isn’t good.” Streep so relished her debut in a film musical that, although the vocals were prerecorded at Air Studios, she insisted on singing her part on set from first thing until the last take at night. “I’m not sure if the sound guys were picking it all up by that time,” Craymer says, “but she was still going.”

As for the boys, Firth was once in a band and can run his left hand over a fret-board. Skarsgard auditioned down the phone to Andersson, who says: “He can sing, although he doesn’t feel so himself.” Apart from the Irish pub songs he caterwauled in his film Evelyn, Brosnan last sang in The Wizard of Oz. It was his first job, as an ASM at York Theatre Royal, and he was in the chorus, at the back. Laying down his vocal track at Air Studios was therefore more terrifying than any 007-related stunt work. “I thought, ‘The hour is upon you here, Brosnan.’ And what gave me the greatest confidence was the look on Colin Firth’s face as he walked through the door. Then Stellan Skarsgard. They looked like men about to take a long walk on a short plank.”

In short, Mamma Mia! is a film in which everyone is making a debut of sorts. That across-the-board inexperience will percolate onto the screen either as freshness or as incompetence. The recipient of more Academy Award nominations than any actor alive thinks she knows which side of the line the movie will fall. “A lot of film-making is done by the seat of your pants,” Streep contends. “People say, ‘Now we know what it is, because it’s told us.’ Few directors, producers and writers come to a film with such a huge gestation of the material behind them. They know its build and its architecture better than anybody that’s usually coming to a film. These girls knew what they had.”

Mamma Mia! is released on July 11

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