The first time Don DeLillo saw his play Valparaiso performed in public, he got a big surprise. It had taken eight years to get it to the stage, after he abandoned it half-finished in 1991 to work on Underworld — the door-stop masterpiece whose publication in 1997 turned him from a cult American novelist into a literary superstar. And yet in all that time, from first idea to sitting in on rehearsals, one thing had eluded him. “I’d written quite a strange play,” he says. “That hadn’t occurred to me until I saw it with an audience.”

Chances are that the average theatregoer will reach that conclusion rather faster than its author when the show makes its British bow in Islington tomorrow. Valparaiso is the story, told in a series of interviews, of Michael Majeski, an ordinary Joe who gets on the wrong plane one day. He knew he was heading for a town called Valparaiso — but was that Valparaiso in Indiana, Valparaiso in Florida or Valparaiso in Chile? Somehow, this botched business trip turns him into a celebrity: journalists question him as if it were the most life-changing mishap imaginable; a Chorus intones flight-safety mantras in a setting that the stage directions describe as “an eerie fluorescence that suggests the hyperreality of a filmed TV commercial potentially viewable in a thousand cities, at 20-second intervals, day and night, for an indefinite period of time”. Strange? You don’t say.

But DeLillo’s playful depictions of the competing realities of the modern world have made this former advertising copywriter a name to bandy alongside those of Updike and Roth, in status if not style. Underworld alone has sold more than a million copies worldwide. Awards were piled on to earlier novels such as Mao II (1991) and White Noise (1984). Admirers such as Dave Eggers, Zadie Smith, David Foster Wallace and Jonathan Safran Foer all owe him a big literary debt.

Yet this will be the first British production of any of his three published plays. And even now, at the age of 69, he is wary of considering himself a proper playwright. “I’m not sure how it all began,” he says in a gentle New York cadence, “except that it was roughly 20 years ago when I had an idea that seemed to demand a limited space. This was a play called The Day Room. What I saw was characters in an artificial setting, a hospital that is not necessarily a hospital: it wasn’t the kind of reality a novelist imagines. And I knew at once that this could not be anything but a play. And of course it’s happened only several times in my life as a writer. But in each case there seemed to be no doubt that I was headed toward the stage rather than toward the printed page.”

Stranger still, the London premiere is being put on at the 60-seat Old Red Lion pub theatre, by a 24-year-old former film student, Jack McNamara. When McNamara approached DeLillo’s agent, he was told not to get his hopes up. Undeterred, he faxed DeLillo a 15-page outline of the approach he wanted to take. Months passed. Then, finally, DeLillo got in touch to give the production his blessing.

They chatted on the phone, then later in person, when McNamara flew over to meet him in a bar in Manhattan. DeLillo says he was impressed by McNamara’s grasp of the play — but also admits that this was the first time that he’d received a serious proposal from a British theatre company.

Speaking on the phone from his upstate New York home, DeLillo is courteous but cautious. He lives with his wife Barbara, an investment banker turned landscape designer. They have no children. He gives few interviews — his first one wasn’t until 1979, eight years after his first novel, Americana, was published — but he’s not, he insists, a recluse. More a lone wolf. “The writer,” he once said, “is the person who stands outside society, independent of affiliation and independent of influence.” So he’ll talk candidly, charmingly, amusingly about his work — and offer a dry rejoinder or a Pinteresque pause if you push much beyond that.

Valparaiso had to be a play, he says, because he felt that the story needed to be told after the event, in interview form. The characters speak in a deliberately stilted, artificial way, as if jargon were the only tie that binds them together. “In my plays I seem to write dialogue that’s quite different from the dialogue in my novels,” he says. “It’s less naturalistic, a little more formal.”

Does he accept that he’ll reach fewer people than he would with fiction? “Oh yes. And it simply doesn’t matter. If an idea seems to find its way towards a stage setting, that’s the direction I take. I don’t know if I’m trying to achieve anything other than to follow an idea on to the page or, in this case, into three dimensions, with an actor and an audience. The idea dictates the medium.”

Is he much of a theatregoer? “I’m not avid. I’m much more of an avid moviegoer. But one of the many great advantages of New York of course is theatre.”

A young playwright he admires is Will Eno. “A brilliant mind,” he says. “And a real playwright. Unlike some of us.” So does DeLillo feel he is still earning his spurs as a dramatist? “Yes. It’s not that I set to work tentatively; it’s just that I feel a little tentative about what happens after I’m finished writing. The true work only begins then, and that makes me feel like a perennial newcomer.”

He’s attended rehearsals for his plays, and for John Malkovich’s 1994 stage adaptation of his novel Libra. How does he feel if actors or directors challenge him? A laugh. “For a novelist these are sometimes difficult situations to enter. I think it may be a tendency more likely for American actors. I’ve just been in on rehearsals on a new play now in Chicago, and I did find myself making some changes based on comments actors made.”