All Woody Allen's best films of the Seventies feature abstract art. In Play It Again, Sam (1972), Allen plays a film critic trying to get over his wife's leaving him by dating again. In one scene, he tries to pick up a woman in front of an early Jackson Pollock work. "What does it say to you?" he asks her. Five years later, in Annie Hall (1977), when the Diane Keaton character goes to see her analyst, he inevitably has an abstract painting on the wall. In Manhattan (1979), Allen's character, Isaac, bumps into his friend Yale and his mistress (Diane Keaton again) and the three argue over photography and the "negative capability" of a steel cube installation's texture. When we get a glimpse of Isaac's apartment near the end of the film, a Mark Rothko painting hangs on the wall.

In the 1960s and '70s, whether you were reading the most fashionable contemporary poets and thinkers in London or were going to an analyst or an art museum in New York, abstract art was on the cover or hung on the wall. Even today, if you want to suggest wealth and sophistication, set designers will reach for abstract paintings. In BBC Two's recent series, The Honourable Woman, the outstanding TV drama of the year, there is a huge Miró painting on the wall in the town house of the Stein Foundation. It tells you that the Steins are not just wealthy but also sophisticated, cultured and cosmopolitan; a Constable or a Monet would convey a very different message. The cluster of images is significant: modern poetry, the New Left, psychoanalysis and, always in the background, abstract art.

However, while Isaac was hanging the Rothko reproduction on his apartment wall in Manhattan, artistic fashion was starting to shift. If you look at the most popular 20 shows at the Tate Galleries in the last 40 years they have almost all been figurative artists. Damien Hirst, Hopper, Gauguin, Cézanne, Turner/Whistler/Monet, Frida Kahlo, Lichtenstein and Constable make up the top ten with this summer's Matisse cut-outs at number one. The only out-and-out abstract artist in the top ten is Rothko at the Tate Modern in 2008. Miró and Kandinsky: The Path to Abstraction are the only other exhibitions of exclusively abstract artists in the top 20.

The Royal Academy and the Tate galleries know that if they want a blockbuster they can't go wrong with Gainsborough, Constable, van Gogh or the Pre-Raphaelites. David Hockney's A Bigger Picture at the Royal Academy attracted 7,512 visitors every day in 2012. You couldn't get near van Gogh's paintings at the RA in 2010: there were queues around the block. You may expect the same at Rembrandt: The Late Works at the National Gallery or Constable: The Making of a Master at the V&A this autumn.

Further down the hierarchy, there are other signs of the revival of figurative art. There is the renewed interest in Eric Ravilious (11 books about his work published since 2002), the discovery of important female figurative artists like Eva Frankfurther, Paula Rego and Dora Holzhandler, and a series of international exhibitions of Chagall last year in Britain, Paris and New York, and of Edward Hopper, on both sides of the Atlantic, over the last decade.

Figurative art has always spoken to a wider audience, and this has spread through British culture in recent years. The last 20 years have seen a number of plays about figurative artists: Pam Gems's Stanley (1996), about Stanley Spencer, Nicholas Wright's Vincent in Brixton (2003), about van Gogh, and Lee Hall's The Pitmen Painters (2007). However, the most popular play about modern art in recent years was Yasmina Reza's Art, a satire about the pretentious appeal of abstract art. It was the emperor's new clothes updated for today's theatre audiences and it ran in the West End for eight years.