Twenty minutes into Mamma Mia! The Movie, I was on the brink of walking out, fidgeting with irritation at the hammy cast, forever squealing and jumping off things – jetties, roofs, beds – and the preposterous plot about who’d fathered some old hippy’s love child. But I stayed, and two hours later found myself outside the cinema in larky high spirits wondering when I might go again.

What curious magic does Mamma Mia! weave, that more than 30 million people have seen the stage show? And now the third most successful musical of all time has just leapfrogged Harry Potter to become the most successful British movie at the UK box office.

The key, of course, is the music of Abba, the disposable pop which, 30 years after it was written, still fills our iPods. Björn Ulvaeus, neat, bearded, with that polite, detached Scandinavian inscrutability, has long tried to figure out exactly what he and his partner Benny Andersson did to grant themselves pop immortality.

“Someone said there is champagne in the music – bubbles,” he says. “But Bobby Gillespie of Primal Scream said the songs manage to combine a melancholic feeling with a euphoric feeling. That is interesting and true because the songs are very often in minor keys and the lyrics are very often sad, but still the sound is uplifting.”

As Abba lyricist, Ulvaeus is responsible for the ultimate break-up anthem, The Winner Takes it All – belted out on screen with raw power by Meryl Streep – besides that unintentionally hilarious line in Super Trouper: “I was sick and tired of everything/ When I called you last night from Glasgow.” But listening to Abba’s mightiest (and only American) number one, Dancing Queen, the fact the girl is “young and sweet, only 17” is shadowed by a tristesse in the melody, enjoining us to celebrate this moment because the girl will not be 17 for ever. Sort of “gather ye rosebuds while ye may” with synthesizers.

For Andersson and Ulvaeus, the “Abba sound” was their obsession. They created a “wall of noise”, with rich and intricate arrangements, overlayering the voices of the female singers (Ulvaeus’s wife, Agnetha, and Andersson’s, Anni-Frid) into multiple harmonies. They were studio perfectionists and innovators as much as Phil Spector or the Beach Boys but received none of their kudos. “We always had the latest high-tech stuff,” says Ulvaeus. “We’d hear a sound on a record. What is that? We had to have it.”

But this technical complexity sucked the fun out of performing. “It was great having the audience there, but we were reproducing exactly what we did in the studio. With groups like Led Zep and the Stones, when they’re on stage different things happen. But we had a big band and a set list of songs to play and there was no room for improvisation. It all had to go together in order to produce that Abba sound. We weren’t really a band of musicians, we were a vocal group with musicians. But above all we were writers and producers.”

It’s little wonder, then, that Abba hated touring. They virtually invented the music video to be broadcast on chart shows so they wouldn’t have to turn up in person. Indeed tour-phobia is the prime reason Ulvaeus, now 63, refused $1 billion in 2000 to reform the band. The frenzy of their 1977 tour, with screaming Australians besieging airports and mad crushes at concerts, was captured by Lasse Hallström in Abba: the Movie. For Agnetha and Anni-Frid, who were the faces – or in the former’s case the famously shapely bottom – of the group, the pressure was intense and intrusive. Moreover this was no normal band. Since the two couples were married, there was no escape from fellow band members after-hours and both had children – Frida had two from an earlier marriage and Björn and Agnetha had a daughter, Linda, and later a son, Christian – whom they either brought along or pined for.

At first, it was assumed their relationships were a gimmick “like one of these manufactured bands”, says Ulvaeus. “When, in fact, Abba was completely organic.” Indeed, Andersson met Ulvaeus in the Sixties, playing in rival groups on the Swedish circuit, became close friends – as they are to this day – and co-opted their fiancées, both minor solo artists, into a new band called Festfolk, meaning “engaged couples”. It seems almost extraneous to say that, renamed Abba after their first initials, they won Eurovision in 1974 with Waterloo, beginning a string of catchy but never cool hits until their marriages, and then the band itself, fell apart around 1982. Did working together somehow hasten the split? “Abba kept our marriages intact for much longer than if, say, the girls had been touring and we had been in bands with two other guys,” Ulvaeus insists.

While he and Agnetha were divorcing, he wrote The Winner Takes It All and wonders if the lyrics, “The winner takes it all/ The loser standing small/ Beside the victory/ That’s her destiny…” helped fuel her subsequent Garbo-esque mystique. “She sang it and people were thinking she was abandoned and lonely – oh poor Agnetha.”

Of the four she is certainly the most private, seldom leaving Sweden because she refuses to fly after Abba’s chartered plane hit a storm. But far from some bitter rift, they even celebrated last Christmas together. And at the Swedish premiere of Mamma Mia! The Movie, the quartet were seen together in public for the first time since they dissolved. “We were standing in the lobby, all four of us just talking and after a couple of minutes it felt like yesterday,” he says. “It seemed completely natural. They are both wonderful women, so it makes it easier.”

If you want to survive pop superstardom, it helps to be Swedish. Ulvaeus lives quietly now in Stockholm, reads, sees his children – three of whom live close by – and looks after his youngest grand-daughter, aged seven months. He seems serene and relaxed, his legacy assured. But even at the apex of Abba-mania, while British schoolboys debated whether they most fancied the blonde or brunette, Sweden left their biggest stars alone. “We could go to the local shops in Stockholm without being harassed. It was very much an ordinary life. Walking down the street, knowing everyone knows who you are, but no one turns their head,” Ulvaeus chuckles. “And if someone does, it’s a foreigner, a tourist.”

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