Meryl Streep is one of the most cerebral film actors alive; a professional of effortless intellectual calibre. A true measure of her greatness is that she does not feel remotely threatened by taking accessible or entertaining roles.

Hence the pleasing story of how the queen of intelligent movies came to be involved in Mamma Mia!, the new film based on the musical, in turn based on Abba songs - which opened four days ago and which, if it does not quite infect the world at the speed of Spanish flu, will probably be experienced by as many millions.

It was in the dreadful days just after 9/11, Streep explained to BBC Radio 4, that she decided to take her daughter and friends to see Mamma Mia! the musical to cheer them up. By halfway through, they were seduced - stomping and cheering along with the rest of the audience. Afterwards Streep, thrilled at how the evening had worked such life-enhancing magic on sad families, wrote a fan letter to the cast. And, such is the way of these things, when they came to make the film version, they asked the great one if she would play the lead role. She agreed.

The result is an uninhibited, fun, cheesy, hugely tongue-in-cheek women's film that has, as few others have done, parted the critics like the Red Sea. The highest-browed men, poor things, entirely missing the irony, have struggled to cope with Streep in a popular role, or to find words hate-filled enough to describe the result: “absolute cack”; “silliness unredeemed by wit or polish”; “super pooper... soulless panto”; “hideous... a crock of hooey”; “Streep meets her Waterloo”. My colleague James Christopher, the Times film critic referred to “Hollywood blancmange” and said that the “sight of a Greek conga of local scrubbers vamping to Dancing Queen on a wobbly wooden pier is a truly terrifying spectacle”.

And there was me thinking what fun it would be if I was part of it.

Never have the posh male critics been marooned higher or drier. They have missed the joke, you see. Almost everyone else in the world, it seems - especially women - got it. People love this movie despite its flaws. They love that it celebrates middle-aged women; that it laughs at itself continuously; that it is shamelessly silly and heart-warming.

The city centre audience with me on Friday night cheered, laughed and clapped; when I got home, even the erudite guests on Newsnight Review proclaimed it as an entirely new genre of post-post-postmodern ironic cinema, describing it as perniciously effective, and confessing that they loved it too. All of which is proof, were proof needed, that few mortals can withstand the power of the music of Abba, which is the pumping heart of Mamma Mia! and remains the most phenomenally enduring back catalogue of pop music in the world: the soundtrack, in fact, to the lives of most of us.

There is brilliance here - classical craftsmanship of a level that has proved itself again and again. Abba are not the Beatles, but only because they are, in many ways, bigger and better. But there is something more going on here than a critical schism over a cheesy movie: it is an authentic question about the time that it takes great popular culture to be recognised as real art - and the prejudice that persists over it even then. Are we so blind that we cannot see the greatness - and cleverness - in accessible entertainment? Why can't we be confident enough to ignore the snobbery that decrees anything with mass appeal (apart from football) is simply awful?

Matthew Parris put his finger on it acutely on these pages last week when he saluted the brilliance of Dolly Parton, a singer sneered at for years as some kind of ridiculous hick.

Instead, as he so rightly pointed out, she is a hugely talented artist (and a rather wonderful person too, I think) whose voice had the power to move him to tears. Forget the kitsch - Parton is a singer with immense, life-enhancing power whose art bears comparison with the great opera performances. But it has taken a 20-year time lag for us to realise this. Twenty years of snobbery and condescension.

Who rated Abba 25 years ago? Few people that I knew. They preferred Tom Waites. Enjoying anything as easy or as sentimental as Abba meant that you had to join the masses; you were not part of an elite. And so, to appear cool, we pretended to despise some of the best music written. But the music endured, and its rhythms and combination of sad lyrics and uplifting tunes - what the lyricist Tim Rice calls true genius - has proved us all wrong. This is not dumbing down. This is remembering that the true purpose of art should be to entertain, not to prop up some kind of exclusive club. One is not stupid or compromised if one is uplifted by popular music or drama; nor should one be cowardly in admitting it.

Had Shakespeare or Joyce or Dickens or Puccini been sitting in Cineworld with me watching Mamma Mia!, they would have nodded thunderously with approval and left the cinema muttering: “I want a piece of that.” Had Ibsen been there, he would have been up on his seat applauding Streep for empowering middle-aged women. Which other stars and artists, once sneered at, will be recognised as true cultural classics? It's already started with Ian Fleming, once derided as a writer of pulp fiction, now recognised as one the best novelists of the past 50 years.

Here are a few more suggestions. Simon Cowell, a genius of entertainment, and his whole Pop Idol genre. Robbie Williams, whose Angels will feature in singalongs in old folks' homes for the next two centuries. Elton John. Coronation Street, future course material for sociology undergraduates. Friends, ditto for its portrayal of a terminally narcissistic society. Katie Price, aka the model Jordan, the closest we have to a modern day Wife of Bath.

For Meryl Streep is right. In a world so crippled by anxiety about how we should live our lives and uncertainty about where we are going, there is no shame, and much benefit, in simple, unpretentious fun.

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