The classics and class have always been uncomfortably linked. In the history of this country’s education system, knowledge of the classics was traditionally the gatekeeper of privilege. If you acquired the classics you gained a passport to the establishment. Fail and the corridors of power remained out of reach. And, despite a vigorous history of working-class autodidacts - such as one Alfred Williams, born in 1877, who taught himself Latin and Greek by chalking up irregular verbs in his forge - the gate has remained largely shut to the working classes. It is no coincidence that the high-watermark of the British Empire, and that of British classical learning, were more or less coterminous.

Even the words ‘classics’ and ‘class’ derive from the same root; the Latin classis comes from the verb calo, to summon. A classis is a group of people ‘summoned together’. It is a word associated with Servius Tullius, one of the early kings of Rome, who was supposed to have conducted the first census. The men in the top six classes were classici. By the second century AD, the term classici came to be used of the most distinguished authors – the scriptores classici.

But the baby has been thrown out with the bathwater. The impulse in the latter half of the 20th century was, instead of broadening access to the study of ancient languages, to strangle it slowly, at least in the state education sector. The result is that Latin and Greek have become more the preserve of independent and public schools, and their inevitable poster-boy Eton-and-Balliol man Boris Johnson. With splendid paradox, the Government does not recognise Latin - the progenitor of a handful of modern European tongues - as a language, as far as the national curriculum is concerned. A quota of just 27 PGCE places is available nationally to would-be Latin teachers each year, and there are a mere eight places for those on graduate on-the-job training schemes.

And along with the insidious identification of the study of classics with a certain social class has also come a popular notion of the classics as somehow inherently the property of the political right. This is no accident, of course, Johnson himself is a Tory. The classics prodigy Enoch Powell created an infamous identification between classics and the right when he summoned up the shade of Virgil in his ‘Rivers of Blood’ speech. The study of Latin has, in Catholic countries, been necessarily identified in the past with the rigidities of the Church. When French students took to the barricades in Paris in May 1968, one of the injustices they protested against was the compulsory study of Latin. Even now, the right in Britain are more sympathetic to the claims of the classics than their Labour colleagues. For the post-Blair Labour party, the classics are damned because they stink of privilege and are, worst of all, regarded as irrelevant to ‘modern Britain’.

What is so bewildering about this popular notion, however, is how little it reflects the daily practice of the classics by professional scholars. You can find right-wing classicists, of course, but it is miles easier to come across classicists whose work contributes to ideas on the left. You might think of the pioneering work of feminist classicists, which has been important since the birth of the women’s movement and beyond (it was Jane Harrison who quoted Terence in support of the suffragists). Meanwhile, research on Greek homosexuality continues to make an important contribution to ideas within the gay rights movement. Numberless ideas from the ancient world - from Sparta to Athens’ radical democracy - have been reeled in by the left. Gilbert Murray, perhaps the greatest British classicist and public intellectual, was Liberal, not Conservative in his politics. Today, thoughtful work abounds by scholars, such as Joy Connolly’s on Cicero, with its underlying critique of US society under the Republicans.

In the arts world, the arguments about ‘elitist’ or ‘relevant’ culture are, thankfully, tired and outmoded. But they haven’t always been. When Labour was elected in 1997, the Government poured cash into the arts, but at the same time berated them for elitism and inaccessibility. The policy arguments were beaten out over the course of a decade. First, under former culture secretary Chris Smith, the arts were seen to be contributing to the economy as part of the ‘creative industries’. Then, the justification was all about the arts’ instrumental uses – the arts can help in literacy, and healthcare, and make children more aspirational, was the argument. Gordon Brown likes the idea of the arts as knitted into our national life, part of the glue that can hold us together against the divisive forces that threaten to drag us asunder.

But in the end all these arguments about use skirt around the main issue. It had to be acknowledged that the arts are important not just because of the money that they help bring in from foreign tourism, or because singing in the choir helps a class of primary school children’s discipline, but because they have some intangible, transformative power that resonates in our very souls. They inspire and delight us, disgust and frighten us, speak to our dreams and nightmares. This kind of personal stuff is hard to articulate, least of all in a political context, but the arts have managed to do it.

A similar task faces classicists who wish to see their subject embraced by politicians. Classicists can always argue about the uses of classics – that, like the arts, their study improves literacy and discipline; or that they help students understand grammar or learn modern languages; or that knowledge of the ancient world is crucial to understanding the institutions and structures that enfold our lives today. All these arguments are important, and should always be part of the arsenal – but they will invite objections. In the end, Latin and ancient Greek are unspoken ancient languages. They are not, in fact, particularly ‘useful’ in day-to-day life. And why should they be ‘useful’? Have we not found that ‘useful’ people, those busy bankers and financial regulators, have fallen short, somewhat?

The value of the classics, like the value of the arts, is difficult to articulate, verging on the intangible. Their value is about their very remoteness from ordinary life – the fact that they can provide a place where the intellect can range freely over subjects taken more or less in the abstract, rather than snagging on the barbs and hooks of the everyday. Their value is that they offer a playground for the imagination, in which our very disconnectedness from ancient Greece and Rome invites the willing mind to elaborate the gaps and lacunae. Their value is that they are removed from our busy, relevant, modern society and from the forces that conspire to factory-make mini-consumers in the guise of educating our children.

Charlotte Higgins is the chief arts writer of the Guardian. Her books are Latin Love Lessons and It’s All Greek to Me. Her next book, for Jonathan Cape, will be about searching for Roman Britain.