Here’s a funny thing about the musical Mamma Mia!. It is a bona fide global phenomenon. Thirty million people have seen it and sung along to Abba’s songs. It has made $2 billion at the box office, and played in 160 cities around the world. Yet when I got two free tickets for the London show, I couldn’t persuade a single person to go with me. Not one. Ooh, sorry, if only you’d given me more notice, my colleagues lied. Lucky you! Wish I could make it, said friends, running gratefully for the hills. So why is it such a success? Who goes to see it? And how did they persuade Meryl Streep to star in the forthcoming film version?

The answer to all these questions lies in the immaculately groomed person of Judy Craymer, the show’s originator, producer and, now, self-styled gatekeeper. Craymer, 50, lives in a fabulous penthouse flat in Knightsbridge, where Diptyque candles burn in every room and ranks of silver photograph frames march across the surface of the grand piano. An attractive blonde in a black dress and black leather jacket, with a white Chanel watch, she has an immaculate manicure and immaculate bare, brown legs. She is, in fact, well-camouflaged among the tasteful Kelly Hoppen-ish black, white and taupe decor. Given the wariness with which her charm is tinged, that could be the plan.

She rarely gives interviews, because there is rarely any need: Mamma Mia! is a juggernaut that has been rolling since opening night, back in 1999.

“We’re hoping to create pure pleasure,” said director Phyllida Lloyd at the time. “We’re not splitting the atom.” They obviously succeeded; by 2005 it was the most successful musical in the world.

Now, there is the film. Hollywood came calling years ago, but Craymer, Lloyd and the writer, Catherine Johnson, refused to sell the rights. If Mamma Mia! was going to become a film, they were going to do it when they wanted and on their terms. Hollywood invariably wants Hollywood directors and producers but, miraculously, they managed to keep hold of the film themselves. The feat becomes even more unlikely when you consider that none of them had ever done anything remotely on the scale of a Hollywood movie before. But faced with a take-it-or-leave-it attitude, Universal decided they wanted the film enough to take it. The one concession was an experienced American producer, Gary Goetzman.

“They wanted to keep the essence of what it is,” Craymer thinks. “The big thing was convincing them it was going to be a great film, and that we weren’t just making a musical into a film.”

It’s a long way from Craymer’s roots as a jobbing producer working on shows such as Cats and Chess, with stints in film and TV also on her CV. Born and bred in North London, she had studied stage management and music at the Guildhall School of Music & Drama, always knowing that she wanted to be behind the scenes, not on stage. After graduating, she worked for a rep company in Leicester alongside Cameron Mackintosh – “He was broke too then!” – who was making his name with touring versions of My Fair Lady and The Rocky Horror Show. She lived in an unheated house, showered at the theatre, earned £30 a week, and loved it.

Then, in 1982, when she was 23 and working for Tim Rice on Chess, she met the men who would change her life: Abba’s Benny Andersson and Björn Ulvaeus, who were writing the songs for Chess. Though not much of an Abba fan – Led Zeppelin, T.Rex and punk were more her thing – she nonetheless had a hunch that Abba songs would work in a musical. The only problem was persuading Benny and Björn to let their songs, of which they were fiercely protective, be used.

“If I hadn’t known them and had that relationship with them, there’s no way the idea would have been taken seriously,” she says. She already had the bones of the plot – two generations of people, a holiday, a wedding. What she needed was someone to pull it together and write a script. Step forward Catherine Johnson, the third piece of the puzzle who, with Craymer and director Phyllida Lloyd, became the holy trinity responsible for Mamma Mia!.

“I was working with a writer and director called Terry Johnson,” remembers Craymer, “and asked if he’d like to write it. He said, ‘No.’ He regrets that now,” she adds, deadpan. “He suggested Catherine, and she and I had this long meeting where we stuffed our faces with sandwiches at some Sherlock Holmes place near Selfridges. Just as we were ending, at 4 o’clock on a winter’s day, she said, ‘Have you thought of a mother and daughter?’ and I said, ‘Ooh, fantastic!’ So we sat back down and ate more sandwiches.”

With hindsight, Craymer says, it’s easy to look back and think it was all just great fun. “But there wasn’t anything at stake. We weren’t earning any money for it, we weren’t going to lose a job. The whole idea [at that stage] was to get Björn and Benny to say yes, and they hadn’t yet.”

Johnson wrote a feel-good story, Shirley Valentine meets Muriel’s Wedding, set on a Greek island, with a bit of mystery, a happy ending and, of course, Abba’s greatest hits. She and Craymer went round to Björn’s place near Henley and pitched the script: he said yes there and then.

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