It was lunchtime, and in a large, high-ceilinged room with fluted pilasters a long line of aging men in dark three-piece suits — actors playing veterans of the Burma campaign in World War II who have gathered to hear Mountbatten (Charles Dance) deliver a commemorative address — were lining up in front of a buffet. Most of them wore plastic bibs to prevent the food from spattering their costumes. “A sea of white men,” said Morgan, who is 56, taking in the scene from a table on the other side of the room. “Imagine the prostate issues in here.” It was a characteristic remark from a writer ever alert to the humanizing frailties of political heavyweights. Short and slight, with tired, pale blue eyes and a mischievous grin, Morgan is himself an unimposing figure. His face has a certain gallant plainness to it. As an undergraduate at the University of Leeds, he briefly tried acting; had he pursued a career in front of the camera, he might have found work playing a World War I Tommy or, later, a retired footballer. He wore a black coat over a polo-neck sweater into which he kept dipping his chin, like a turtle retreating into its shell. He rarely gives interviews. “I absolutely deplore being written about,” he said. “I don’t want anyone to know who I am. When I see writers going on too many TV shows, I think, You’ve got to be careful you don’t become part of an establishment. Becoming part of an establishment is the death of creativity.”

Morgan prefers to disappear into his work. When I asked Colman if she had any funny stories from her time collaborating with him, she paused to think. “Not really,” she said at last. “He isn’t a drinker, so he never does that sort of bumbling-twat thing at a party. If anything, I’ve been the one doing that.” Being a showrunner, Morgan told me, is like having multiple full-time jobs (writing, casting, editing, looking in on set), so he always feels he is neglecting one or more of his duties. While Season 3 was being filmed he was busy writing Season 4, which will cover the years of Margaret Thatcher’s premiership. “His brain is in constant motion,” the actress Gillian Anderson, who will play Thatcher, told me. “We are all in awe and slightly afraid of it in equal measure.” She and Morgan have been dating since 2016. They first met when Anderson appeared in “The Last King of Scotland,” the 2006 film about the rise of the Ugandan dictator Idi Amin, for which Morgan co-wrote the script with Jeremy Brock. (He has five children with his first wife; the couple separated in 2014, after 17 years of marriage.)

Morgan rises early every day and sits down at his desk around 6 a.m. Hours will pass in fruitful silence. Unlike others in his line of work, however, he is not incorrigibly solitary. Once a week, a team of researchers, which doubles as a kind of writers’ room, comes over to his house in Central London for script meetings, based in part on documents they’ve dug up pertaining to whichever episode he happens to be working on. These could be anything from contemporary press clippings to transcripts of original interviews with those who witnessed, or participated in, the events he is in the process of imaginatively reconstructing. “He’s not precious about the material,” Annie Sulzberger, the show’s head of research (and the sister of The New York Times’ publisher, A.G. Sulzberger), told me. “As a researcher, you find a detail and you think, Wow, I hope this makes the cut. That doesn’t mean anything to him. If something doesn’t move the plot along, or reveal character, or tell us something relevant about Britain at the time, it doesn’t have a place.” Morgan isn’t precious about the scripts themselves either. “If something isn’t working in rehearsal he’ll say, ‘Can you hang on a minute? Just talk amongst yourselves,’ ” Colman told me. “Five minutes later it’ll be, ‘O.K., try that.’ And sure enough he’s just churned out a brilliant speech.”

After lunch, we descended to one of the building’s entrance lobbies, where Christian Schwochow, the director on the episode, was setting up a shot involving Dance and Rupert Vansittart, the actor who plays Cecil King. The men in three-piece suits, now without their plastic bibs, were milling around holding dimpled beer mugs and cigarettes. Morgan’s mind was elsewhere, however. A few days earlier, Schwochow had shot what was supposed to be the episode’s final scene, in which Mountbatten, having been dressed down by Elizabeth for even entertaining the thought of a coup, pays a visit to his ailing sister, Princess Alice. It’s a poignant, faintly surreal encounter, two superannuated grandees coming to terms with their own obsolescence, but Morgan felt it didn’t quite work as an ending. Instead, he suggested to Schwochow and Oona O’Beirn, a producer on Season 3, the narrative ought to return to Elizabeth, who has spent most of the episode abroad boning up on the latest developments in racehorse breeding, her principal passion in life, with Lord Porchester, an old friend for whom, it’s intimated, she once harbored romantic feelings.