One of the distinctive aspects of British culture is that the word "intellectual" seems to be regarded as a term of abuse. WH Auden summed it up neatly when he wrote: "To the man-in-the-street, who, I'm sorry to say, / Is a keen observer of life,/ The word 'Intellectual' suggests right away/ A man who's untrue to his wife."

Auden wasn't alone in thinking that intellectuals suffer from ethical deficiencies. The journalist and historian Paul Johnson once devoted an entire book, Intellectuals: from Marx and Tolstoy to Sartre and Chomsky (2000), to proving that some of the 20th century's most prominent thinkers were moral cretins. And in his book The Intellectuals and the Masses (Faber, 1992) the literary critic John Carey argued that most of our culture's esteemed thinkers over several centuries despised the masses and devoted much of their efforts to excluding the hoi-polloi from cultural life. Both Johnson and Carey were pushing at an open door. Britain is a country in which the word "intellectual" is often preceded by the sneering adjective "so-called", where smart people are put down because they are "too clever by half" and where a cerebral politician (David Willetts) was for years saddled with the soubriquet "Two Brains". It's a society in which creative engineers are labelled "boffins" and kids with a talent for mathematics or computer programming are "nerds". As far as the Brits are concerned, intellectuals begin at Calais and gravitate to Paris, where the fact that they are lionised in its cafes and salons is seen as proof that the French, despite their cheese- and wine-making skills, are fundamentally unsound. Given this nasty linguistic undercurrent, a Martian anthropologist would be forgiven for thinking that Britain was a nation of knuckle-dragging troglodytes rather than a cockpit of vibrant cultural life and home to some of the world's best universities, most creative artists, liveliest publications and greatest theatres and museums.

The fact that a nation that lives by its considerable wits should be in denial about its reliance on the life of the mind is truly weird. It's what led the historian of ideas Stefan Collini to postulate what he calls the "absence thesis". This has two dimensions – temporal and geographical. In the first, contemporary figures are regarded as just pale reflections of the great figures of the past: thus Christopher Hitchens and Martin Amis, say, are pygmies compared with George Orwell and Aldous Huxley. Richard Posner, another student of public intellectuals, describes this as measuring today's average against yesterday's peak. In either case, it conveniently ignores the fact that the heroes of the past were often undervalued by their contemporaries as mere pale reflections of the "really" great figures of an even more distant past. The geographical dimension of the absence thesis is reflected in the belief that intellectuals begin at Calais. But, as Collini observes, "the frequently encountered claim that there are no intellectuals in Britain is generally advanced by those who, were they living in certain other societies, would unhesitatingly be regarded as intellectuals".

As a historian, Collini smells an ideological rat here, and traces the odour to an ideological belief in British exceptionalism. What it amounts to is the belief that the course of British history has been so exceptionally smooth – with its adaptable aristocracy, (relatively) tolerant church, apolitical military and reformist bourgeoisie – that there was no call for the evolution of an oppositional intelligentsia. So the fact that there are no intellectuals in Britain is something to be proud of. It's a byproduct of the Whig interpretation of history.

This strikes me as baloney, mostly derived from a comprehensive misunderstanding of other cultures – a species of what Collini calls "Dreyfus envy", after the celebrated late 19th-century affair in which intellectuals took on the French establishment and won. Intellectuals may enjoy a higher celebrity status across the Channel but I can see little evidence that France is more governed by ideas than is Britain. Part of the problem is that our stereotypical image of the public intellectual is a continental one – and largely embodied by Jean-Paul Sartre and his long-time accomplice, Simone de Beauvoir. The fact that (as we discovered after their deaths) they were devious, manipulative, hypocritical and – in Sartre's case at least – ludicrously credulous about authoritarian regimes has tarnished their lustre somewhat. But much the same could be said of many of the other public intellectuals of yesteryear: think of Arthur Koestler, who specialised in treating people abominably while writing the sublime Darkness at Noon, or of the British intellectuals of the 1930s who so admired Stalin, even as he was slaughtering his own people.

So let us cast off the inferiority complex towards the cerebral continent and move on to more interesting questions. What, for example, is a public intellectual? In his study of the species, the American legal scholar Richard Posner defines them as "intellectuals who opine to an educated public on questions of… political or ideological concern". It's not just enough to be interested in ideas, therefore; to count as a public intellectual (or PI, for short) one must participate in debate to clarify issues, expose the errors of other public intellectuals, draw attention to neglected issues and generally vivify public discussion. The French polymath Pierre Bourdieu saw PIs as thinkers who are independent of those in power, critical of received ideas, demolishers of "simplistic either-ors" and respecters of "the complexity of problems". The Palestinian literary critic Edward Said saw the public intellectual as "the scoffer whose place it is publicly to raise embarrassing questions, to confront orthodoxy and dogma, to be someone who cannot easily be co-opted by governments or corporations".

None of these definitions is sharp enough to be very useful: any ranter with a megaphone and a mastery of rhetoric could qualify. In his book Absent Minds: Intellectuals in Britain (Oxford, 2006), Collini goes to the other extreme, arguing that a public intellectual is someone who first achieves a level of creative or scholarly achievement and then uses available media to engage with the broader concerns of wider publics. So the novelist Ian McEwan, say, would qualify but a widely read newspaper columnist might not.

What this highlights is the intrinsic imprecision of the concept of the public intellectual. Faced with this, most analysts of the phenomenon fall back on measures of the impact that individual thinkers make on the public consciousness. In his survey of American public intellectuals, Public Intellectuals: a Study of Decline (Harvard, 2003), for example, Posner had the plausible idea of trying to rank over 500 candidates who had been prominent between 1995 and 2000, using media mentions, web hits and scholarly citations. But he immediately ran into the problem that the third metric wasn't appropriate for many of them. The Nobel laureate Gary Becker had over 5,000 scholarly citations while the New York Times columnist David Brooks had none, but who is to say that Brooks is the less influential intellectual?

But at least Posner did his own research. Most other surveys of public intellectuals seem to be done by polling readers of highbrow publications. For example in 2004 Prospect magazine conducted a poll to find "Britain's top 100 public intellectuals". This produced the usual suspects (Tariq Ali, Melvyn Bragg, Terry Eagleton, John Gray, Christopher Hitchens, Lisa Jardine, Roger Scruton, George Steiner) but also a few left-field candidates (the musician Brian Eno, for example, as well as TV executive David Elstein and Robert Cooper, the cerebral diplomat who was the brains behind Tony Blair's doctrine of interventionism).

Four years later Prospect teamed up with the American magazine Foreign Affairs with the aim of identifying "the 100 most important public intellectuals that are still alive and active in public life". The resulting list was compiled via a readers' poll and purported to be global, so perhaps it wasn't entirely surprising that only eight Brits (Kwame Anthony Appiah, Richard Dawkins, Salman Rushdie, Christopher Hitchens, Martin Wolf, Tony Judt, Niall Ferguson and James Lovelock) figured on it. But the more one examined the list, the wackier it seemed. For example, it suggested that the world's greatest living public intellectual was Fethullah Gülen. Eh? Wikipedia reveals that he is "a Turkish preacher, author, educator, and Muslim scholar living in self-imposed exile in Pennsylvania". No 3 was a guy called Yusuf al-Qaradawi, who is apparently an Egyptian Islamic theologian, while No 5 was a Pakistani barrister named Chaudhry Aitzaz Ahsan and No 7 was Abdolkarim Soroush, an Iranian Islamic scholar of whose existence I had until that point remained blissfully unaware. I could go on but you will get the point. Recognising that they had been shafted by some clever flash-mobbing, the erudite editors of Prospect and Foreign Affairs tried to salvage something from the wreckage in a later edition. Noting that the definition of public intellectual remained "satisfyingly vague", they set up what the racing fraternity would call a stewards' inquiry to "weigh up the field on three criteria: novelty, real-world impact, and intellectual pizzazz". The result: the world's leading intellectual turned out to be General David Petraeus, architect of the US "surge" in Iraq, currently in charge of the fiasco in Afghanistan and scheduled to become head of the CIA in September.

This is the kind of thing that gives superficiality a bad name. How, for example, would one measure novelty, let alone "intellectual pizzazz"? But if public polling is vulnerable to the kind of ballot-stuffing that made nonsense of the Prospect/Foreign Affairs survey, and if Posner's more rigorous metrics are inadequate, is it possible to come up with any listing of significant public intellectuals that is not, in one way or another, arbitrary?

In an attempt to answer the question, I tried a different tack by analysing the lists of contributors to serious English-language print or online publications (including the London Review of Books, the New York Review of Books, major broadsheet newspapers, some widely read blogs and other sources), looking for British thinkers. I then added to these the names of British intellectuals drawn from earlier surveys by Prospect and Posner. The result was a list of just over 300 people (grouped by their primary profession) whose ideas are deemed worthy of public attention by the gatekeepers of the publications I surveyed.

A list like this has a certain voyeuristic fascination, and will doubtless be seen as arbitrary by those who find themselves – or their favourites – excluded. It also comes with a health warning. Compiling it makes one realise how difficult it is to make an assessment of the impact that any particular individual has on the public consciousness. The philosopher Onora O'Neill has influenced the thinking of many of us with her coruscating insight. But so too has the playwright Michael Frayn. Both have had a significant impact on our culture. But who has been more influential? Impossible to say. Similarly, with his Radio 4 series In Our Time, Melvyn Bragg has done sterling service in injecting serious ideas into public consciousness. Is he therefore a more significant public intellectual than the unobtrusive editor of the London Review of Books, Mary-Kay Wilmers? Who knows?

So a list like this is a starting point for a discussion, not a conclusion. It raises some intriguing questions. Take the gender balance, for example. Only around a quarter of the intellectuals listed are women. Does this mean that British cultural life is unusually male-dominated? Actually, it suggests the opposite. Only 9% of the list of the world's "Top 100 intellectuals" produced by Prospect and Foreign Affairs were women. And of Posner's list of 546 public intellectuals just 10% were women. The other intriguing feature of our list is the relative importance of different professions. (Again, this comes with a caveat, because in many cases it's not easy to determine what the "primary" profession of an individual is: many intellectuals write both fiction and non-fiction, for example – which is how Hilary Mantel and Jonathan Raban find themselves in the same category: authors.)

But if the list is anything to go by, then the dominant professions from which contemporary British public intellectuals are drawn are journalists (20%), writers (19%), historians (14%) and critics (13%).

A big surprise is the relatively poor showing of thinkers whom one would expect to be making a significant impact on public discourse – philosophers (4%), scientists (4%), economists (3%) and politicians (2%). But the main conclusion to be drawn from this survey is that the trope that intellectuals begin at Calais is simply wrong. The British aversion to the I-word seems to be at odds with the facts. This country has an impressive array of lively, creative and argumentative minds. And if you doubt that, just watch them take this thesis to pieces.

Britain's top 300 intellectuals: the list