THERE was an interesting trajectory to the trailer that introduced William Ivory's big BBC4 drama, Burton and Taylor, this week. It was a story, the announcer proclaimed, of devotion, divorce, destruction, and despair.

That might be an effective formula for drama, but it also tells us something about how love is understood in contemporary culture.

The tempestuous on-off love affair between Elizabeth Taylor and Richard Burton was a celebrity soap opera for more than two decades. She was "the most beautiful woman in the world", commanding Hollywood's biggest salary. He was one of the most celebrated Shakespearean actors of the day, with a Welsh-burred voice like liquid gold. They were both married to other people when they met on the set of the 1963 epic Cleopatra, and became locked into an affair so scandalous that the Vatican branded it "erotic vagrancy".

The fable was fed by the extravagance of Burton's gifts of jewellery to Taylor - the Krupp Diamond and the 50-carat La Peregrina pearl - as well as the excess of their drinking and public cat-fighting, which, after ten years of stormy marriage, ended in divorce in 1974. Notoriously, although they couldn't live together, they couldn't live apart, either. Later, they remarried, then re-divorced.

The BBC4 bio-pic joined the story at their third reunion in New York, for a run of Noel Coward's Private Lives, a play in which a divorced couple meet by chance. Ivory's Burton and Taylor muse in an after-show supper on the essential qualities of a marriage: passion, they begin; then sex, they agree; then trust, Burton says. . . At which point the conversation breaks down.

Taylor, in the play, offers a masterclass in emotional manipulation. Burton is no match for a woman whose skills range from little girl lost, through dumb broad, to intuitive theatrical genius, woman wronged, and Machiavellian schemer. Burton feels he can separate the personal and the professional in Private Lives, but Taylor knows that the audiences who bought $2 million-worth of seats before the play even opened were hoping to see an on-stage reprise of the couple's most famous film, Who's Afraid of Virginia Woolf?, in which a couple trade insults in front of their dinner guests. This was theatre as freak show.

What is on offer here is a view of love as something that never grows beyond romantic infatuation. It is the default mode for love in popular culture, where, once the rush of adrenalin fades, it is time to move on. Taylor had eight marriages, one fewer than Zsa Zsa Gabor, who once said to me in an interview: "People say I am promiscuous, darling, but I never slept with anyone to whom I was not married. . ."

It is interesting to note that Taylor and Burton had no children. Parental love is a window into the many other kinds of love that develop when the thrill of the chase is complete. "Where did my Anthony go?" Taylor asks in the play, bringing fiction and fact into the confusion. "The beginning of love", Thomas Merton, said "is the will to let those we love be perfectly themselves, the resolution not to twist them to fit our own image."

Ivory's Burton concludes by telling Taylor: "I love you and I always will. . . But, you and I, we're addicts." To which she ripostes: "Love is not a drug." The plays suggests that, to some people, it is. And that is a myth that spreads far wider than one mad, bad pair of star-crossed lovers.

Paul Vallely's new biography Pope Francis: Untying the knots is published by Bloomsbury this week.