“The Motive and the Cue,” a new play in London, imagines fraught behind-the-scenes maneuvering by John Gielgud, Richard Burton and Elizabeth Taylor during rehearsals for a classic Broadway production.“The classicist who wants to be modern, meeting the modernist who wants to be classical.” So says Elizabeth Taylor, summing up the fractious encounter between the revered Shakespearian actor John Gielgud, and her new husband, the actor Richard Burton. It’s 1964, Taylor and Burton are the most famous couple in the world, and Burton is rehearsing the role of Hamlet for a Broadway production that Gielgud is directing.It’s not going well.That’s the setting for “The Motive and the Cue,” a new play directed by Sam Mendes, written by Jack Thorne, and starring Mark Gatiss as Gielgud, Johnny Flynn as Burton and Tuppence Middleton as Taylor.The play, which opened to enthusiastic reviews in May and runs through July 15 at the National Theater, in London, was an idea born out of the pandemic, said Caro Newling, a co-founder with Mendes of Neal Street Productions, which developed the show.Newling said that, during the first coronavirus lockdown of 2020, Mendes was thinking about why theater mattered, and what went into creating great performances. When they were discussing those questions, she added, Mendes recalled reading a copy of “Letters From an Actor,” an account of the 1964 “Hamlet,” by William Redfield, who played Guildenstern in the production. “Suddenly, bang, this idea shot out,” Newling said.A 1964 photograph shows Richard Burton, left, and John Gielgud in a rehearsal for “Hamlet.”Getty ImagesThe idea was a play based on the fraught relationship between the rambunctious, hard-drinking Burton and the repressed, elegant Gielgud during rehearsals for “Hamlet,” with the added combustible element of a sidelined, glamorous Taylor, sitting out her honeymoon in a hotel suite.Newling and Mendes started researching, and discovered another out-of-print book: “John Gielgud Directs Richard Burton in Hamlet,” a fly-on-the-wall account by Richard Sterne, an ensemble actor who smuggled a tape recorder into the rehearsal room.Mendes called Thorne, the playwright behind the stage blockbuster “Harry Potter and the Cursed Child” and the television series “His Dark Materials,” and suggested the rehearsal dynamics might provide fruitful material.Initially unsure, Thorne found a focus by “understanding the position that Gielgud was in at the time. He wasn’t being loved by the public, treasured by the profession. His great rival Laurence Olivier was running the National Theater and a new kind of modern theater was dominating the West End. He took the Broadway job because he didn’t have other offers.”“Hamlet,” had been a defining role for Gielgud, who had played the part over 300 times. For the Broadway “Hamlet,” he came up with the idea — daring at the time — of doing the play as if it were a rehearsal run-through, in ordinary clothes. In “The Motive and the Cue,” Burton tries to stamp his brash personality on Hamlet, while the classicist Gielgud wants something more sensitively attuned to Burton’s deeper emotions.The cast of “The Motive and the Cue.” Jack Thorne, who wrote the play, said it was about “why we do what we do, what it feels like, and what it costs.”Mark Douet“What’s interesting is that Burton is getting it wrong, sort of on purpose, trying to show Gielgud that it must be modern,” said Flynn, who lived as a teenager in Wales, where Burton is a national hero. “I had a picture of him playing Hamlet on the door of my house for about 15 years,” Flynn said. “It felt eerie that now, I was playing him, playing Hamlet.”The irony of the Burton-Gielgud conflict, he added, was that Burton idolized Gielgud, and was desperate to be regarded as a serious actor. “He is incredibly successful, but deep down, he fears he has drifted into complacency, is not doing something valuable with his art,” Flynn said.The set, designed by Es Devlin, uses expanding and contracting scrims to create seamless transitions between the “Hamlet” rehearsals, a pink hotel suite in which Taylor and Burton throw glamorous parties for the cast and the scenes of more intimate encounters. One of these is between Gielgud and Taylor, who provides the psychological insight that allows the director to find a way to Burton.Middleton, who plays Taylor, said, “Elisabeth is the voice of reason, one of the wisest characters in the play.”“She completely understood Burton’s obsession with conquering Hamlet, and why it was so difficult for him.,” she added. “It was important to me to show she wasn’t this chaotic, floozy character she is sometimes seen as.”Tuppence Middleton as Elizabeth Taylor in “The Motive and the Cue.” The play is set shortly after Taylor’s marriage to Richard Burton.Mark DouetMuch of the play is concerned with how to play Hamlet: The breakthrough moment for Burton happens when he can connect his painful past to the character’s motivations. “This is what actors have to do when they strip themselves down to play a role,” Thorne said.In the end, the 1964 production was a triumph, running for 136 performances; “The Motive and the Cue” has been a hit, too. It is currently playing to sold-out houses and its popularity suggests that the play’s central ideas — theater as a community and a crucible of emotional connection between actors and audience — have resonated after the enforced closures of the last few years.“It’s about fathers and sons, classicism and modernity, the clash of these forces,” Thorne said. “But I hope it’s also about why we do what we do, what it feels like and what it costs.” More