One of the funniest and most trenchant critiques of Parisian existentialism takes place in the 1961 film The Rebel, in which Tony Hancock plays a deluded would-be artist who has quit the stifling mediocrity of East Cheam for the delights of avant garde Paris. Having accidentally found himself the new darling of the Left Bank, Hancock is invited to a fashionable party by a busty, kohl-eyed woman in a tight black polo-neck sweater. She huskily intones gnomic gems such as, “Why kill time when you can kill yourself?” Hancock gawps at her in bafflement. “I’m an existentialist,” she goes on, by way of explanation. “All of my friends are existentialists.”

The lad himself is unimpressed. “Well, it’s company, innit!” he finally says, barely disguising his gentle derision. It is hard to imagine a more delicious cultural collision than this, or one that so effectively captures how – to the sceptical English eye – French philosophy, for all its fag-waving sexiness, is also mostly pretentious and daft.

No philosophy has exemplified this more than existentialism, the movement that dominated cultural life in Paris after the second world war. The word was first used in prewar Germany to describe the kind of philosophy, propounded by Martin Heidegger and Edmund Husserl, that argued existence in itself was meaningless and morality was a fiction. The Parisian generation led by Jean-Paul Sartre first met these ideas in 1930s Berlin while studying metaphysics, or during the lectures given by the Russian émigré Alexandre Kojève on Hegel and the master-slave dialectic in Paris. What made French existentialism so new and unique was that it tried to marry what was fundamentally a form of nihilism with the French tradition of ethical thought. This was a generation of thinkers and writers, including big names such as Albert Camus, Simone de Beauvoir and Raymond Aron, who combined deep moral seriousness with commitment to literature, politics and the real world.

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Having written a book called How to Live: A Biography of Montaigne, and obviously deeply steeped in French thought, Sarah Bakewell is expertly equipped to tell us the story of existentialism. It helps that she writes well, with a lightness of touch and a very Anglo-Saxon sense of humour. So it is, for example, that she charmingly introduces us to her 17-year-old self, a self-styled “suburban existentialist”. There is sadly no mention here of discovering existentialism” (as I and many others did) by reading about the Cure in the NME (their early single Killing an Arab was a naked A-level steal from Camus). But she is aware that, as much as anything else, existentialism was also a fashion and style, and that the real life of those who called themselves existentialists in the 1950s was mainly lived outside the university seminar.

The spiritual headquarters of the movement was Le Tabou, a nightclub on the Rue Dauphine. Jazz provided the soundtrack to the hard-living, free-loving lifestyle of the student followers of Sartre and his acolytes. The often unisex clothes were mainly black and casual. A popular satirical song of the 1950s celebrated “the little existentialist” with her black trousers and flat shoes, and her “look so fatalist”. From a 21st-century vantage point, existentialism – like most faded youth subcultures – can now seem out of date and profoundly silly.

Existentialism is really about making choices. How to live? How to be free? How to be an “authentic” human being?

This is not, however, a silly book and it is sometimes very profound indeed. Bakewell’s deepest aim is to resurrect and re-examine existentialism as a way of thinking that can transform reality; this is what separates existentialism from more abstract philosophies. She begins with the old undergraduate chestnut about whether existentialism is a mood or a philosophy. The correct answer is of course that it is both, often at the same time. More to the point, behind the subculture, the sensationalism and jokes, existential philosophy was inspired by the recent and real crises of war and occupation in France in the mid-20th century.

Bakewell is a skilful and nuanced teacher. Her explanation of the mysteries of phenomenology, clear and succinct, is as brilliant as any I’ve heard in a French university classroom. For the uninitiated, phenomenology is a philosophy of German origin that focuses on the world as it appears (“phenomena”, in Greek, means “things as they appear”) rather than questioning the interpretations of reality. In the hands of the French existentialists, this means, as Bakewell puts it, a philosophy that goes “straight to life”. This is what makes existentialism so passionate and exciting, whether you are a 1950s Left Bank starlet or, as in Bakewell’s case, a lost teenage girl in the 1980s.

The author offers fascinating insights into the cultural impact of existentialism on the English-speaking world. In his influential 1957 essay The White Negro, for example, Norman Mailer predicts much of what would become the counterculture, saying that this is the making of what he calls “the hipster” or “the American existentialist”. English existentialists included the young Iris Murdoch, who got Sartre to sign her copy of Being and Nothingness and wrote to a friend of “the excitement – I remember nothing like it since the days of discovering Keats and Shelley and Coleridge”.

Less breathless was Colin Wilson, who became a literary star in the 1950s when the publication of his first book The Outsider, written in Leicester and London, briefly made him the Albert Camus of the Midlands. Wilson was 24 when the book came out, and with his floppy hair, turtleneck sweater and provincial accent, he was a perfect fit for the role of angry young man. His book was wild and inaccurate and he irritated publishers by thinking of himself as a genius (in his self-delusion he was in many ways the prototype for the Tony Hancock figure in The Rebel). But The Outsider was also thrilling. Most importantly, it introduced a generation of young British readers to European ideas and how daring they could be.

Existentialism, in all its incarnations, is really about making choices. How to live? How to be free? How to be an “authentic” human being? In her summing-up, Bakewell makes the case that these questions remain as important today as they ever were. Seeing the rise of irrationality on all sides, she asks whether freedom may prove to be the great puzzle of the 21st century. That is why she is so right when she wonders if, in the new age of bad faith, “we need the existentialists more than we thought”.

At the Existentialist Café is published by Chatto (£16.99). Click here to order a copy for £12.99