In new works by English playwrights, the 45th U.S. president plots to become the 47th, and the New York urban planner Robert Moses loses his mind.LONDON — Donald J. Trump won’t surrender the spotlight easily. But few could have guessed that he would find renewed life on the London stage, where Mike Bartlett’s scattershot satire, “The 47th,” opened last week at the Old Vic and will run through May 28.Why the number 47? Because the play takes off from America’s 45th president angling anew for top office in 2024. His appetite for attention remains undimmed, as does a fondness for golf. Bertie Carvel, whose portrayal of Trump is the play’s banner achievement, is first seen chugging into view on a golf cart: an impressive entrance that starts the play on a high.Dismounting to launch into a lengthy soliloquy bemoaning “four years of lonely exile,” the character before us looks and sounds uncannily like the man himself. Embodying a public figure 30 years his senior, Carvel — clearly padded — captures Trump’s outsize swagger and bullishness, alongside his ever-busy hands and that strangely fey voice. The tilted head and near-constant squint are perfectly caught, too.But those expecting the sort of “Saturday Night Live”-style broadside familiar from Alec Baldwin are in for a surprise. Within minutes, the audience is aware of a character, not a caricature, and one with a lot on his mind. The opening monologue depicts a vengeful figure acutely aware of how he is regarded: “I know, I know, you hate me,” this Trump remarks at the start.Promising “plans and plots aplenty,” Trump comes across as a Richard III for our time in a blank verse play that tosses out Shakespearean allusions like confetti. Seething with resentment but mindful of his dynasty, Trump gathers his three eldest children to search, like Lear, for an heir to a political kingdom he won’t lose without a fight.The play, to its credit, views Trump in three dimensions, and grants him a way with words you certainly wouldn’t expect from those lips in real life. “It’s not like you to coyly act the mute,” he tells Ivanka (a sleekly coiffed Lydia Wilson), a Cordelia equivalent reluctant — as in “King Lear” — to voice the affection that her father should already know. And I laughed out loud at this Trump’s dismissal of Machiavelli’s “The Prince” as too long — as if he would have opinions about a 16th-century political treatise.Joss Carter as the Shaman and Lydia Wilson as Ivanka Trump in “The 47th.”Marc BrennerWhen Carvel is center stage, “The 47th” entirely grips. The problem comes with a rambling, shapeless narrative that soon loses its way. It’s as if Bartlett were so busy trying to cover all bases that he leaves too many untended. (He’s certainly busy, with three plays running simultaneously in London.)The family drama, for instance, soon gives way to a portrait of an increasingly turbulent America whose anger has only intensified since the storming of the Capitol last year. Bartlett concocts a new slogan — “America rules” — that is emblazoned on banners spilling from the upper reaches of the theater to put us in a rallying state of mind. Miriam Buether’s set is itself quite plain: a blank canvas for a bellicose electorate.The imagined 2024 presidential race finds a sleepwalking, ailing Biden (a raspy-voiced Simon Williams) ceding center stage to Kamala Harris (the American actress Tamara Tunie), whom Trump duly treats with contempt. “You’re an ugly person,” he tells her. “I’m sorry but you are.” In fact, Tunie is so immediately classy and capable a presence that you wish she were given more to do.As well as characters we all know already, Bartlett presents some new ones, including Rosie (Ami Tredrea), a Republican, who derides her brother Charlie (James Cooney), a Democratic journalist, as “desperate and corrupt.” Rupert Goold’s production elsewhere brings on a QAnon-style Shaman (a furious Joss Carter) as a reminder of the darker forces that threaten democracy. Thrashing about in fury, he signifies a gathering anarchy that is also summoned by Ash J. Woodward’s video projections depicting mob misrule.Reuniting the team behind another play that peered into the immediate future, Bartlett’s “King Charles III,” this latest exercise in prophesy sags whenever Trump leaves the stage. His energy — however malign — is the motor that keeps it going, and Carvel certainly has my vote.Trump requires little introduction. But that might not be the case with Robert Moses, the Yale- and Oxford-educated urban planner and designer who died in 1981, age 92. His story famously informed the vast 1974 biography “The Power Broker,” by Robert Caro, and has now spawned a more streamlined play, “Straight Line Crazy.” Written by the English playwright David Hare, this exposition-heavy drama brings Ralph Fiennes roaring back to the stage as Moses and is running at the Bridge Theater through June 18.Ralph Fiennes as Robert Moses in David Hare’s “Straight Line Crazy,” directed by Nicholas Hytner at the Bridge Theater.Manuel HarlanAnyone who has made use of the highways and bridges in the greater New York area has probably traveled a route made possible by Moses, a hugely renowned figure in his day. A visionary who overflowed with ideas about how to reshape public spaces and the ways people obtain access to them, Moses attracted criticism as well. Although he didn’t drive himself, he was hostile to public transportation, not to mention casually racist and heedless of the communities displaced by the realization of his grand schemes. (One highway included bridges with deliberately inadequate clearance, so buses couldn’t use them.)Hare chooses two decisive points in Moses’ life to tell a story of vaulting ambition that devolves into the madness hinted at in the play’s title: 1926, as Moses, not far from 40, proposes building two parkways to link New York City to Long Island, and, after the intermission, 1955. The idea then was to build a sunken expressway that would cut through Lower Manhattan’s Washington Square Park.Fiennes has enough barrel-chested authority to sustain interest in what might otherwise seem arcane. You almost wish that the play, and Nicholas Hytner’s adroit production, were longer and amplified the material more. Moses’ nemesis, the urban space activist Jane Jacobs (Helen Schlesinger, struggling with the accent), gets a crucial speech at the top of the play, but this self-described warrior isn’t shown putting up much of a fight.The other characters — various employees of Moses included — largely pale next to the momentum that builds as Moses starts to break down. “I’d rather be right, and alone, than soft, and with other people,” he admits toward the end, showing the Trump-like megalomania that brings a piecemeal play to hurtling, powerfully acted life.The 47th. Directed by Rupert Goold. Old Vic, through May 28.Straight Line Crazy. Directed by Nicholas Hytner. Bridge Theater, through June 18. More