Following the deaths of Bergman and Antonioni, is this the end of the auteur?

First Ingmar Bergman, and then Michelangelo Antonioni – the death this week of two of the towering figures of post-war European art- house cinema can't help but seem like a portent. It signals the near-end of a tradition. There is a dispiriting sense that the two deceased directors were among the last of a breed. The old-style "auteurs" are fast disappearing.

Their impact was once enormous. The British film-maker Mike Leigh has talked about his experience of arriving in London from Salford in the autumn of 1960 and immediately being "blasted from here to eternity by the French cinema, the Italian cinema, the Russian cinema, the Japanese cinema, the cinema of Satyajit Ray, etc". In other words, the cinema of auteurs. His experience was far from unique. Many other future directors from his generation speak in equally rapt terms about encountering Bergman or Renoir or Rossellini for the first time.

They evoke an era when London was awash with repertory cinemas. You could start at the National Film Theatre on the South Bank, and then venture outwards. There was the International Film Theatre in Westbourne Grove. ("That's where I remember seeing Jules et Jim. That was a traumatic experience because, at that time, I was deeply in love with someone who was in love with somebody else. It was a very emotional experience," Leigh recalls.)

Then there was the Academy in Oxford Street, where the 16-year-old Michael Apted saw Bergman's Wild Strawberries for the first time. "It was a total epiphany. I realised that a film could carry serious ideas. Up till then, movies, to me, had been about following girls and having popcorn entertainment. This, in a sense, changed my whole life."

The passing of Bergman and Antonioni is a reminder that such cinemas – where their work was most likely to be found – no longer exist. Of course, their films are available on DVD – and, in that respect, more accessible than ever. However, there has been a huge change both in where we see films and in the way in which films are made.

The UK currently has a thriving independent cinema business. In recent years, plenty of enterprising young distribution companies (Optimum, Vertigo, Dogwoof, Soda, Revolver, etc) have sprung up, all ready to give theatrical releases to the best foreign-language films and the most challenging documentaries. The UK Film Council has set up a P&A (prints and advertising) fund to help these distributors get their movies into cinemas.

There are great hopes now for broadening British cinema-goers' fare through digital distribution. The UK box-office successes of seemingly " difficult" foreign-language films such as Pan's Labyrinth and Amores Perros suggest that British audiences are far more adventurous than they are given credit for. Even so, none of this has done anything to protect that near-extinct species, the "auteur".

Liv Ullmann, one of Bergman's muses, freely acknowledges that the kind of European art-house cinema that Bergman stood for is now in its death throes. "It is dying out," she said when I interviewed her at the time of the release of the Bergman-scripted Faithless (2000). "Young people say that it is like filmed theatre. Quick cuts and camera angles – they think that's film. That is not film.

"Film is to show people and life, and to make you know more about life than when you went in. It's not this cut, cut, cut, kill, kill, kill, sex, sex, sex..."

One shouldn't overlook the fact that a huge amount of self-indulgence and pretentiousness went hand in hand with the "auteur" tradition. It was in the pages of Cahiers du Cinéma, in the early 1950s, that the idea of "auteurism" ("la politique des auteurs") was first expressed. At the time, it was a polemical tool as much as a measure of aesthetic worth.

François Truffaut and his irreverent young colleagues were desperate to attack what they called "le cinéma de papa", by which they meant hidebound, literary film-making from an older generation. They championed as auteurs not just Europeans such as Max Ophüls, Roberto Rossellini and Vittorio De Sica, but also film-makers that others saw as Hollywood-studio journeymen, such as Allan Dwan, Raoul Walsh, Budd Boetticher. For them, these were film-makers with a strong lyrical and personal style.

There was a confusion at the heart of the auteur tradition from the outset. The Cahiers critics were often inconsistent in their criteria. Truffaut – the admirer of Balzac – was the most literary of film-makers himself. His films weren't so very different from those scripted a few years before by Jean Aurenche and Pierre Bost – the targets of his bile. Jean-Luc Godard was an admirer of Bergman's Summer Interlude, despite its traditional, sometimes stagey storytelling style.

Still, for audiences, it was clear who the real auteurs were: film-makers such as Bergman, Antonioni, Truffaut, Godard, Rossellini, Agnès Varda, Rainer Werner Fassbinder and Krzysztof Kieslowski, whose movies turned up in such numbers at their rep cinemas. Their work was likely to be strongly personal, with many of the same themes recurring from picture to picture. The films were unlikely to have been expensive to make. In the case of the more prolific directors, such as Fassbinder, they could be rough around the edges.

None the less, there was a devoted audience who would go to see the " new Bergman" or the "new Truffaut" on trust. They didn't need to be lured by aggressive marketing campaigns. They were keen to debate the films.

Of course, it is easy to posit a golden age of art-house cinema that never really existed, and to wax overly nostalgic about fleapit cinemas. One of the less lofty reasons why Bergman and Antonioni were popular with British cinemagoers was their frank treatment of sexuality. In the early 1950s, when the Brits were making Doctor in the House and Trouble in Store, Bergman was directing films such as Summer with Monika, featuring nudity and an unrestrained depiction of the characters' erotic lives. Bergman was embarrassed when The Silence (1963) turned into a succès de scandale, with audiences swarming to see it in search of titillation.

One leading contemporary British film-maker admits that he found the work of Antonioni tedious in the extreme. "Apart from the fact that every heterosexual young man I knew, including me, only ever went to see them because they wanted to fuck Monica Vitti, there was no appeal. Red Desert was just the depth of arty bollocks. It was devoid of irony and the humour of life."

The Italian director had a rare knack of provoking extreme reactions in unlikely quarters. He had passionate admirers, but his work also infuriated many. "It was the worst picture that I ever saw," the Hollywood star James Caan said of his film Zabriskie Point, in an interview. "I got so angry about it. I was in love with a girl. We went to the movie and it ended the whole affair. He [Antonioni] hired cardboard, the worst actors, and it was a conscious effort – that's what pissed me off!"

No one can deny that the cult of the auteur masked a lot of mediocre and self-indulgent film-making. Nor can you overlook the perversity in ascribing so much influence to one person – the director – for work that was often collaborative. Stars have always been far more of a pull for audiences than directors. Nonetheless, when Bergman and Antonioni were in their prime, audiences were ready – and eager – to engage with their work.

This May, the Cannes Festival celebrated its 60th anniversary by commissioning a series of short films by today's leading directors. As the roll-call attested, there are still plenty of visionary film-makers telling personal stories. Walter Salles, Lars von Trier, David Cronenberg and Jane Campion, among many others, contributed to the venture. There was even a very entertaining silent short from the 98-year-old Portuguese director Manoel de Oliveira – by some stretch, the oldest old-school auteur still in business – imagining a meeting between Khrushchev and the Pope.

None the less, it will take more than a series of short films to revive the cult of the "auteur".

Bergman's heirs: The new wave of auteurs

Lukas Moodysson

"A young master's first masterpiece," Bergman commented of his fellow-Swede Moodysson's debut, Fucking Amal. However, Moodysson's more recent films, such as Container and Hole in my Heart, have baffled audiences.

Andrea Arnold

The British director won the inaugural Bergman award this year for her debut feature, Red Road. She cites Tarkovsky, the Dardenne brothers and Bresson as inspirations.

Lars Von Trier

The ageing enfant terrible of European cinema isn't really young enough to be included here, but he is one of the few contemporary film-makers whose name is as recognisable as those of the auteurs of the past.

Michael Winterbottom

Having made documentaries about Bergman, Winterbottom shares his work ethic: with his producer Andrew Eaton, he has already built up a substantial body of work.

Lynne Ramsay

Ramsay proved herself a distinctive director with Ratcatcher and Morvern Callar. Then, thanks to the vagaries of British film financing, her career stalled. Now she's back, with an adaptation of Lionel Shriver's We Need to Talk about Kevin in the works.

Aleksei Balabanov

Russian critics rave about Balabanov, a saturnine figure whose works range from box-office hits such as Brother to grim dramas about the Chechen war. His latest film, the ultra-violent Cargo 200, has left a trail of controversy.

Harmony Korine

The boy-genius of US indie cinema in the 1990s made a startling first impression, scripting Kids and directing Gummo and Julien Donkey Boy. Then he seemed to lose his way, but he's back now with Mr Lonely.

François Ozon

The inventive, versatile Ozon self-consciously follows in the tradition of directors such as Fassbinder. His latest, Angel, starring Romola Garai and Charlotte Rampling, is his most ambitious yet.

Jaco Van Dormael

Having won plaudits for Toto le héros and The Eighth Day, the Belgian Jaco van Dormael is now working on one of the most expensive films in recent European history, Mr Nobody, his first film in a decade.

Jonathan Glazer

Glazer made his name directing Guinness ads, but is now one of contemporary British cinema's most visionary and distinctive talents. The reputation of his feature film Birth is bound to grow.