What do you do after turning yourself into Julia Child, a bold, occasionally bossy woman who changed the way people think about food? You turn yourself into Margaret Thatcher, of course, an even bolder and bossier one, who changed the way people think about Britain. This is what Meryl Streep does in “The Iron Lady,” which opens Friday in New York. In yet another of her miraculous impersonations, which has already been nominated for a Golden Globe award, she seems even more Thatcher-like than Mrs. Thatcher, so that after the movie if you go back and look at photographs of Mrs. Thatcher in her prime, you can’t help feeling that they’re a little off. She no longer looks like herself. Sitting over tea recently at the Waldorf Astoria with Phyllida Lloyd, the film’s director, Ms. Streep said that she had been hoping to make a movie about Elisabeth Kübler-Ross, and that Ms. Lloyd told her sarcastically, “Yeah, that will pack them in.” But when offered the role of Mrs. Thatcher, Ms. Streep didn’t hesitate. “You have to imagine yourself as a 62-year-old actress getting a phone call asking you to play the first female leader in the Western world elected on her own merits and not on the coattails of her husband,” she said. “To say, ‘No, I’m not interested’ would just be ridiculous. There is no other opportunity like it.” Ms. Streep researched her part carefully enough to learn even what Mrs. Thatcher carried in her handbag: 3-by-5 cards with adages by Kipling, Shakespeare, Abraham Lincoln and Disraeli. She also realized, she said, that Mrs. Thatcher, who is now 86 and in ill health, was herself an impersonation of sorts, a woman who allowed herself to be made over by Tory strategists and even changed her way of speaking. In the movie Ms. Streep effortlessly imitates those burnished, sometimes strident, declamatory tones, the one the novelist Angela Carter once said were reminiscent “not of real toffs but of Wodehouse aunts.”

Ms. Lloyd said: “Meryl just has an ear. There’s a Margaret Thatcher voice that British impersonators — men in drag — like to do, and it’s a frightful parody. But nobody has really gone inside it the way Meryl has.” Ms. Streep also captures Mrs. Thatcher’s icy imperiousness, especially toward the end of her career, when she enjoyed humiliating her ministers, and even the hint of sexiness that kept so many of those ministers in thrall for so long. In one scene Ms. Streep is in an evening gown, having a button sewn on before an important Tory function, and when the seamstress is through she hoists her bosom, like Queen Boadicea putting on her breastplate, before going out to challenge a roomful of men. But “The Iron Lady” is not, everyone involved keeps insisting, a conventional biopic, one that follows the career of some exalted personage step by step and ends with him or her in triumph. It’s not even an especially political film. The movie begins in the present, with the Thatcher character old and frail, a little dotty and paranoid, and hallucinating the presence of her dead husband, Denis (Jim Broadbent). She appears that way for almost half the film, revisiting her great days only in memory, so that “The Iron Lady” is a movie as much about decline as about a rise to power. The great events of Mrs. Thatcher’s career — the miners’ strike, the Falklands war, her meetings with Brezhnev (who gave her the Iron Lady nickname) — are touched on only briefly and sketchily.

The movie has provoked strong but mixed reactions in Britain, where some have seen it as a mean-spirited attack on Mrs. Thatcher’s sacred memory, while others have applauded its warmth and humanity. Some Conservative M.P.’s have even called for a House of Commons debate over whether the film shows sufficient good taste and respect. “There have been people who have seen the movie and were fully aghast, who would have liked it to be a triumphalist saga,” Ms. Streep said. “Some in the distribution arm of our own enterprise here were saying, ‘Why can’t we go out on a high?’ ” She changed her voice to sound like an old-fashioned movie mogul. “My God, for 40 percent of the picture she’s an old lady!” She paused for a moment and then changed back to Streep: “That’s the point, you do.” Ms. Streep and Ms. Lloyd (who also directed her in “Mamma Mia”) have by now perfected a kind of “Stage Door” routine together, with Ms. Lloyd — polished, thoughtful — in the Katharine Hepburn part and Ms. Streep in the funny, irreverent Ginger Rogers role. Ms. Streep loves to laugh and also to surprise. At one point, mostly just for the fun of it, she began speaking in the clipped, unnatural voice of a 1930s film star.

“The Iron Lady” was written by Abi Morgan, a British screenwriter greatly in demand these days. She wrote “The Hour,” the “Mad Men”-like BBC serial about television in the ’50s, and together with Steve McQueen, its director, she wrote “Shame,” the new film about sex addiction that despite copious amounts of nudity, male and female, is bleak enough to put most viewers off sex for a couple of days at least. Ms. Morgan said she was initially reluctant to take on the “Iron Lady” project. There had been at least four made-for-TV Thatcher movies fairly recently, she explained — including the well-regarded “Long Walk to Finchley” — and she didn’t think she had much to add. Then she happened to read a magazine article by Mrs. Thatcher’s daughter, Carol, about the moment she realized that her mother’s memory was beginning to slip, and that gave Ms. Morgan the idea of writing about a woman who is starting to fail and at the same time looking back on her life. “What would it be like? I wondered. You’re a woman who was on the world stage and had access to some of the most important decisions in the country, and now to a certain extent you’ve become invisible.” She added: “I really think we will all die while washing up the teacups. Whether you’re Obama or the man in the street, we all die doing those domestic things that we do.” Ms. Lloyd, who is probably better known as a stage director than a filmmaker, said she sometimes thought of “The Iron Lady” as “ ‘King Lear’ for girls.” “Here is this mighty leader reduced to nothing,” she added. “No, not to nothing — to a reckoning with herself.”

Ms. Streep said, laughing: “We’re not interested in King Lear’s politics. We’re not saying we would have voted for him.” She added: “What interested me was the part of someone who does monstrous things maybe, or misguided things. Where do they come from? How do those formulations begin, how do they solidify, calcify, become deficits? How do a person’s strengths become weaknesses? Look at me. I tend to go on too long. I’m a little dogmatic, and that could get really awful over time. If you are self-aware, as actors are, you let these things go into your pores, including criticism. I hate being criticized.” Ms. Lloyd said: “So did Margaret Thatcher. But that’s understandable. She couldn’t show weakness. Imagine what the men would have said.” She added: “In parts of England now it’s a transgression even to consider her as a human being. She’s that monster woman, the she-devil. For me the point of the film was to find the human side.” And though hardly a Tory, she said she vividly recalled the moment when Mrs. Thatcher came to power. “Just as I remember not voting for her, I remember sitting in my room at university when the radio announced that she had been asked to form a government, and I went ‘Yes!’ It felt like one for our team.” Ms. Streep nodded and said: “I did the same thing. We all thought if it can happen in England, class bound, socially rigid, homophobic — if they can elect a female leader over there, then it’s just seconds away in America.”