It is 1993 and, although it didn’t seem so at the time, this was a period of great promise in the Middle East. Under the embrace of Bill Clinton, Yitzhak Rabin and Yasser Arafat shook hands in the White House Rose Garden on a peace deal known as the Oslo Accords.

J. T. Rogers’s award-winning play, first seen in New York, is about the secret process that led to that momentous, now moribund, moment. The historic deal unexpectedly came through the good offices of Norwegian social scientist Terje-Rod Larsen, played here with swaggering sangfroid by Toby Stephens, and his wife Mona Juul, a steely Lydia Leonard.

One of the most highly anticipated productions of the year, the reputation that goes before the play’s arrival here suggests that, in dramatic terms, Rogers has achieved something almost as difficult as the peace process itself — making high drama out of the complexity and nuance of international diplomacy. And indeed, it is hard to imagine a more vivid three hours on this subject than Rogers’s play and Bartlett Sher’s punchy production.

The key here is that the play achieves something comparable to the negotiating methods that Larsen imposes on the talks. It makes human those who are often portrayed as demons.

In the first encounters between the Palestinians — led by Peter Polycarpou’s Finance Minister Ahmed Qurei — and the Israelis, who are ultimately led by Philip Arditti’s clever but arrogant negotiator Uri Savir, we are left in doubt as to the depth of hatred with which each side views the other.

Their first exchanges are insults, fired at each other like howitzer shells. And one of the most convincing portrayals here is of Israeli legal adviser Joel Singer, superbly played by the Israeli actor Yair Jonah Lotan who captures perfectly an implacable Israeli scepticism to the process.

Yet a much more subtle point is made about the foes. When they first share the stage it is impossible to tell which is Israeli and which is Palestinian. And certainly when each side sees the humanity in the other, the intrigue, and tension of high stakes international politics is suddenly given a very moving dimension.

Yet the play doesn’t quite live up to its reputation. It’s a work with the premise that the result was a success. And to maintain that view it therefore has to largely ignore what everyone watching knows — that, today, peace has never been further away. It’s an articulate, often very funny play but it’s a bit like watching a brilliant raconteur tell the most captivating story to an audience who haven’t the heart to tell him his flies are undone. Also, some of the dialogue is downright cliché. “This is our chance to make a difference,” declared by Stephens’s Larsen, is the kind of line that should have been ironed out soon after the off-Broadway premiere. Too often, tension is stoked by having the protagonists square up to each other, only for it to be revealed that they are joking.

Still, it’s refreshing to have a work on the most intractable conflict in the world whose objective is to humanise the characters and reveal the complexity of the situation.

So often, dramas about the Israeli Palestinian conflict are written to deliver a political point of view, which almost always results in a much less interesting play than Oslo.