There is only one musical on everyone's lips, and for a change it's not a Graham Norton and Andrew Lloyd Webber spin-off. Three decades or more after Abba invaded the world's discos, the film version of Mamma Mia! is introducing yet another swath of listeners to the pleasures of Super Trouper and that ultimate producer's anthem, Money, Money, Money.

All the favourites are being brought to the screen next week in a starry package headed by Meryl Streep, Pierce Brosnan Colin Firth and Julie Walters. With its beguiling Greek island setting, the movie is already winning praise as the ultimate escapist treat of the year. Just as the Swedish pop band first cast its spell during the dreary age of stagflation and oil shocks, so the music looks set to carry an adoring public through another era of economic turmoil. Although the sky may be falling once again, everyone can still hum along to Dancing Queen.

That the Broadway version of the show managed to conquer New York in the weeks immediately after 9/11 is some sort of testament to its appeal. Everyone knows how difficult it can be to conquer Times Square, which, on a bad night, can be about as friendly a spot as Omaha Beach. Imagine, then, how much trickier it must have been to launch a frothy, feel-good musical in the city that never sleeps in those sleepless days of autumn 2001.

Yet the formula did the business. Americans may have been traumatised, but they were still willing to be seduced by those maddeningly catchy Seventies anthems. “A giant singing Hostess cupcake opened at the Winter Garden Theatre last night,” wrote a mildly bemused Ben Brantley in his New York Times review. Cupcakes, he added, were what his fellow citizens urgently required at that particular moment, and Mamma Mia! supplied them by the hundredweight.

Times Archive, 1977: Abba

They turned the crusty Albert Hall into a facsimile of a Butlin's holiday camp

Brantley himself couldn't help succumbing in the end: “Mamma Mia! manipulates you, for sure,” he wrote, “but it creates the feeling that you're somehow a part of the manipulative process. And while it may be widely described as a hoot by theatregoers embarrassed at having enjoyed it, it gives off a moist-eyed sincerity that is beyond camp.” Since then, of course, the juggernaut has simply grown and grown, and has evolved into a multimillion-pound franchise (to use that ugly, moneyed phrase), seducing countless spectators who had only the dimmest idea of who Björn and Benny are, or how a generation of overheated schoolboys (myself included) speculated about the respective carnal charms of Agnetha, the glamorous blonde, and the earthier brunette, Frida. The personification of post-Eurovision naffness, the Swedish supergroup enjoyed a new afterlife as the acceptable face of theatrical kitsch.

In the process, Mamma Mia! helped to redefine, for better or worse, the modern musical. Just as Andrew Lloyd Webber had dragged the ailing form back in the direction of pseudo-operatic mega-spectacle, so Judy Craymer's all-conquering hit production reminded impresarios that shows could be marketed as sleek agglomerations of tried-and-tested pop songs.

Critics who long for the more sophisticated tunes and lyrics of Broadway's golden era may find this a depressing phenomenon (will anyone be queuing up to revive We Will Rock You when the last members of the Queen fan club have fallen off their Zimmer frames?) But as jukebox shows go, Mamma Mia!'s portrayal of a wide-eyed young girl's quest on a Greek island is without doubt cleverly crafted.

It at least boasts a storyline, for instance, which is more than can be said of many of its rivals, which tend to be content to dig up old 45s, assemble an energetic set of hoofers and crank up the volume controls in the pit. True, no one is going to mistake Catherine Johnson's plot for The Tempest (although a few sceptics have noted the parallels with the Sixties film Buena Sera, Mrs Campbell, another tale of tangled passions in a lush Mediterranean setting.)

But seeing the writer and the cast find a way of reworking so many tunes into such incongruous settings is like watching a champion exponent of Rubik's Cube put all the colours in the right order inside 30 seconds: not a great aesthetic experience, perhaps, but you have to admire the sleight of hand.

It's easy to appreciate why jukeboxes are in fashion at the moment. The cost of mounting a show in the West End or Broadway grows more prohibitive by the year, and as the musical comedy tradition and the pop market drift farther and farther apart (how many Top 40 hits have come out of musicals lately?) vehicles such as Mamma Mia! are, relatively speaking, a safe investment. Think of how many records Frankie Valli and the Four Seasons have sold on both sides of the Atlantic, and you can only wonder why it took anyone so long to dream up Jersey Boys.

There's an interesting parallel between The Seasons and Abba. Both were an example of a band where the quality of the writing took precedence over personality. How many readers ever knew Björn and Benny's surnames? What mattered most was the smoothness of the conveyor-belt production line. And both bands catered to an audience that was frankly uncool, but couldn't care less as long as the new single had a solid hook.

One other reason why Abba may have survived so many changes of fashion is that their music has some of the sunnier qualities of classic, pre-Sgt Pepper Beatles tunes. It is like listening to McCartney working close to the top of his form, but without Lennon by his side. No, it isn't really as good as the Fab Four, but it has aged better than Wings.

Are the songs in Mamma Mia! great pop music? Personally, I don't think so, and I say that as someone who cheered on Waterloo in front of the TV on the night the Swedes first conquered Eurovision. Moreover, in 20 years of reviewing some of the world's finest pop singers, from Tony Bennett to Norah Jones, I don't recall ever hearing a single Benny and Björn cover.

But, in a way, that's beside the point. Abba's songs are consummately assembled and know exactly which area of the psyche they are aimed at. Against the odds, Mamma Mia! achieves the same weird alchemy.

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