Sophie Heawood: You may be a national treasure, but that doesn't mean you are valued

When John Peel died and a nation mourned, his widow said he would never have believed all the fuss, had he been there to witness it. The same is surely true of Beryl Cook, whose paintings, largely eschewed by national galleries, have been gracing the TV headlines and the front pages of newspapers after the artist's death last week. Cook, who was 81 and had been suffering quietly from cancer, was a shy, working-class woman who preferred to drink in her Plymouth local than accept an invitation to see her paintings hanging in Jackie Collins's home in Los Angeles (though her husband rather fancied making the trip and was a bit annoyed she wouldn't go).

It is in that unreconstructed seafront pub, the Dolphin, that many of Cook's paintings began, as she sketched the good-time girls and the kiss-me-quick sailors who drank there, along with the dartboards, the dogs and the dumpy deliciousness of it all. Her subjects were always fabulously round, their bulbous ankles looking as if they might wobble off their stilettos at any minute. Cook admitted that she hated filling in the backgrounds so she made the people fatter simply to take up more space. The pub is planning a wake to celebrate the life of their best-known customer, whose seat has been empty for the eight months of her illness.

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The locally run Chinchilla Chat Line is in mourning for its animal-loving patron. Plymouth's university and art gallery are discussing a new exhibition of her work. Yet the Tate, that national keeper of the greatest 20th-century artistic jewels, refuses to add Beryl Cook and her much-loved paintings to its London collection. Why? The answer could simply be snobbery. For if Chaucer wrote in the vernacular, Beryl Cook painted in it, and the terrain between high and low culture in this country is still a minefield. Last week, too, there was a hoo-ha after it was revealed that Cambridge University asked English students to compare Amy Winehouse lyrics with a poem by Sir Walter Raleigh. And last month, Katie "Jordan" Price and J K Rowling were guests of honour at the National Book Awards.

Confusion also reigned when Lucian Freud, having also painted a picture of a fat working-class woman, called Benefits Supervisor Sleeping, sold it at Christie's in New York for a record-breaking $33.6m (£17m), the buyer rumoured to be none other than Roman Abramovich. Not widely known as an art collector, Abramovich is one of the Russian billionaires who have come to represent new money like nobody else. While Lucian Freud comes from a family who taught us to interpret our dreams, the new-generation Russians just buy them: Abramovich recently paid all his daughter's favourite pop stars to play at her 16th birthday party. So quite what he wants with a picture of a naked woman from the dole office is unclear, but he wouldn't have paid a 10th of that if it had been painted by Beryl Cook. For Freud has made his "Big Sue" a part of the respected art establishment, whereas Cook's cheery chapesses belong to the masses. And the masses are still a bit of a dodgy lot.

In the US, the author Jonathan Franzen refused to let the TV presenter Oprah Winfrey have The Corrections as her book of the month, seeing himself as highbrow and objecting to having her cheery orange sticker slapped on the cover of all of his books. And then there's the painter Jack Vettriano, who sells by the bucketload and is critically despised. It's not that high and low culture are still miles apart – they have at least turned to face each other – but they're currently facing a nasty stand-off, wherein neither side quite dares to pull the trigger or drop the gun. In the case of Beryl Cook, the art establishment is gravely frightened of dumbing down. And while it's prepared to take a risk with conceptual art, it's much more reluctant to lower the drawbridge towards her figurative sort.

The 20th-century modernists had a different approach to this problem: when the masses started getting educated, the cultured elitists responded by simply making their work more difficult. Virginia Woolf had great disdain for banal women she overheard chatting in lavatories, while Charles Baudelaire dismissed photography as a distraction for the "vile multitude" and T S Eliot reckoned that the spread of education would lead to barbarism. (At least, this is what John Carey pointed out in his 1990 book The Intellectuals and the Masses, though let's ignore the bit where he went on to blame them all for the Nazis.) But before that, writers such as Charles Dickens and George Eliot combined literary and philosophical ideas with sensationalist crime plots; the blend of what would split into high and low culture was seamless. So for our snobbery, it seems, we have the modernists to blame.

Snobbery comes from frustration with somebody else not sharing your desire. Not wanting what you think they are supposed to want. And Cook herself seemingly wanted for little. Perhaps it's that lack of edge, of guile, of motive, that kept her art from turning into something coveted by the biggest galleries. She said she didn't care about being in the Tate and would rather be on birthday cards anyway. "I have nothing I want to say," she once told an interviewer. "I just love painting." Not a declaration that can attach itself to any manifesto: you need an a darker message to be taken seriously in art. Cook is like a pop star who says she just wants to make girls dance.

Of course, you could just argue that her pictures aren't very good. But critique of culture so often comes down to class, not quality, and of belonging to a movement, not working in isolation. Why is Roy Lichtenstein's pop-art take on comic drawing taken any more seriously than hers? Ultimately, Cook's fatal mistake was to represent working-class culture without any tragedy. She spent most nights sitting in the Dolphin with her husband, a couple of beers, and the cards on which she would sketch scenes from life, painting them up at home afterwards in a process that could take months. She was drawn to fun, always drawing larger-than-life characters enjoying themselves, living for the moment. This was working-class pleasure, documented by a working-class woman – and, crucially, it didn't show any grisly endings, nothing to which the adjective "gritty" could be attached. The pictures, widely reproduced as greetings cards and calendars, are funny. Dawn French wrote a comedy show inspired by them; Victoria Wood called them "Rubens with jokes".

In a world before the smoking ban, she depicted everything our current administration wants to regulate against. In our hygienic, sanitised days where people are expected to future-proof their lives, she lovingly commemorated a culture where nobody spots heart disease lurking inside the pickled onions, where fur coats are instruments of seduction, not sadism, and where a puff on a cigarette today carries no hint of lung cancer tomorrow.

Look at that cheeky finger up the bum in Bowling Ladies, and at last week's misguided attempt to stamp out child pornography, wherein our lawmakers have banned the drawing of certain offensive pictures. And would the outdoor boozing be tolerated in Boris Johnson's London? Cook put her paints down only a few months ago, but already her work is a historical document of a time before working-class pleasures were regulated out of existence. And so perhaps history will remember her as a protest singer, her paintings as protest songs.

The Birthday Cake, shows curvaceous nudes snuggled up like cherubim on clouds. Closer inspection reveals they are not in heaven, they are in this life, in a park, eating cake. Naked. Beryl Cook's pictures take the curves and delight with which classical art depicted the next world, but locates that delight clearly in this world. Now that she has gone to the next world herself, perhaps her pictures can take up their rightful place in this one.