In the opening scene of The Iron Lady, an elderly woman walks into a London convenience store, dithers in front of the dairy rack, then buys a pint of milk. The sight of her comes as a shock that never wears off. Though old and frail and addled by dementia, it is unmistakably Margaret Thatcher. Part of the surprise is seeing a legendary icon so enfeebled by age; the other part is seeing her so eerily incarnated by the shape-shifting Meryl Streep. By the end of the film, after watching Streep play the former British prime minister over four decades of her life, the likeness—from the imperious look to the mellifluous diction—is uncanny. Looking not at all like Thatcher, Streep is holding court in a luxury two-storey suite with a fireplace, cathedral ceiling, and a vast bank of windows overlooking Manhattan’s Tribeca district. Her silky hair framing a unlined complexion, the 62-year-old actress looks casually stylish in a long purple jacket cinched with broad belt, black pants and sensible black boots with chunky heels. The suite belongs to the Greenwich Hotel, which is owned by Robert De Niro, who co-starred with Streep in The Deer Hunter, for which she received her first Oscar nomination 33 years ago. After a record 16 nominations, the woman who is routinely called The World’s Greatest Living Actress has won just two Oscars, and has been shut out since Sophie’s Choice (1982). She is overdue. Her tour de force in The Iron Lady, the crowning performance of her career, may be destined to break the losing streak. But at this point does winning a third Oscar really matter? You expect Streep to demur with some modest words about art being its own reward. Instead, her Mona Lisa smile dissolves into a girlish laugh: “I’m very greedy!” she says. Created by Mamma Mia! director Phyllida Lloyd and Shame writer Abi Morgan, both Brits, The Iron Lady does not demonize Thatcher. In fact, she’s less a villain than the fashionatrix played by Streep in The Devil Wears Prada. This Thatcher is a tragic heroine: the grocer’s daughter who becomes an unofficial royal—the stern face of Mother England—stands firm against all foes, only to be left struggling to rule her own mind. “I thought of her as King Lear,” says Streep. “The panoply of her political life, everyone knows that. But we were most interested in how it subsides—in the layers that lie behind that old lady’s face. What are the costs of a life lived so ambitiously? What’s it like to lose the power of concentration, when you were someone who could remember absolutely everything?”

The film’s breathless narrative spans Thatcher’s entire life, zooming through the greatest hits of her rule—the IRA bombings, the poll tax riots, the Falklands war, the miners’ strike. But the story unfolds in flashbacks, anchored in scenes from her 80s, as she drifts in and out of dementia. As Thatcher methodically cracks her boiled egg with a teaspoon at breakfast, she chats away with her jolly, devoted husband Denis (Jim Broadbent), although he’s been dead for eight years. She still can’t bring herself to throw out his clothes. Not unlike J. Edgar, another portrait of overzealous ambition that calcifies into absolute power, The Iron Lady frames its subject with the pathos of old age and impending mortality. Just as J. Edgar tries to humanize Hoover via his doting, lifelong companion, this film softens Thatcher via affection for her husband. Streep, who has never met Thatcher, could study the politician from the public record, but the portrayal of her as a fragile old lady “is completely imagined,” she says. Was Streep not worried about violating dignity? “I did feel responsibility to get that as accurately as I could from my own experience. I don’t think there should be a stigma attached to dementia. My father had it, and I don’t imagine I’m going to be immune. We’re all going there.” Clutching a coffee mug in one hand, she raises her other hand to her forehead. The thing about Streep, whether she’s on screen or sitting across from you, is that her skin is so translucent you can see thoughts and emotions play across her face. “I’m interested in old people,” she says. “I just am. Because I feel myself getting older, and I always have been interested in older people. People who have a big, contentious life behind them, how do they reconcile to the simplicity at the end? To let go of your husband finally, that’s as big a decision as the Falklands.”

The Iron Lady doesn’t open in Canada and Britain until January, but advance screenings and hearsay have already stirred controversy among British conservatives, who feel it’s an un?attering portrait. But some of Thatcher’s left-wing critics may feel it’s too gentle. “She remains hated in many quarters for her policies,” says Streep. “She’s revered in other quarters for how she stood up for what she believed. It’s this discrepancy that attracted me—who is this person who had the ability to withstand that kind of venom?” Streep has long been an outspoken feminist, but when Thatcher became Britain’s first female prime minister in 1979, the actress wasn’t terribly impressed. “I was not a Reagan supporter,” she explains. “I was in the left wing—the actors’ end. The lines are drawn; you don’t cross over. She was from another species, with the bubble hair and the wrong clothes. When she was elected, I had just had my first baby and I was consumed with that. But I do remember having a discussion with my friends that, whether you liked her or not, it was very cool that England—this hidebound, class-driven, gender-exclusive, homophobic, anti-Semitic old boys’ club—had allowed this to happen. We thought it was just a matter of seconds before it would happen in America.” Streep laughs. “Thirty years later . . . ” Despite Streep’s image as Hollywood’s most serious actress, until The Iron Lady Streep had shouldered just two significant dramatic leads in the past 16 years—Doubt (2008) and The Bridges of Madison County (1995). Lately she’s been amusing herself in lighter fare—singing and dancing her way through Mamma Mia!, lazing on the bearskin rug of Alec Baldwin’s chest hair in It’s Complicated, and cooking up a plummy impression of Julia Child in Julie & Julia.

Her Thatcher is another fastidious impersonation, akin to Child, with far more range and gravitas. In researching the role, Streep discovered she wasn’t just playing a politician, but an accomplished actress. The film shows Thatcher being groomed as a performer early in her political career, taking lessons to lower the pitch of her voice, making it less shrill and more confident. Streep, of course, is famous for doing accents, but when she talks about the key to nailing her character, it goes beyond tone and inflection. She had to master Thatcher’s own technique as an actor. “She had capacious breath,” says Streep. “I don’t have anything on her. I’m a trained actress, I have gone to drama school. I’ve attempted Marlowe’s ‘mighty line’ and understood that the best way to read a sonnet aloud is to start at the beginning and don’t take a breath because the breath is the thought and if you carry on to the end of the line you’ll carry the thought.” Streep has now slipped into Thatcher’s rolling cadence as she talks about interviews “in which she would answer a question then ask another, then answer that, and she would go on, and I couldn’t find where she took a breath.” Streep also came to appreciate Thatcher as a woman who crashed barriers of class and gender. “There were things that surprised me when I did the research, because I had my blanket opinions. Given where she came from, just to get into Oxford at that time was very unusual. To take a chemistry degree was unusual. She appointed Jews to her cabinet, which was unusual. There were homosexual scandals, and pressure to fire the people. She said, ‘I don’t care what people do.’ ”

Streep points out that Thatcher’s conservatism belongs to a very different breed than the current U.S. versions. “She was pro-choice, she was an early believer in global warming, she would not disassemble the national health system. All that would make you unelectable as a conservative in the United States.” In watching the soap opera of Republican candidates, she adds, “what really shocks you is how completely unqualified they seem in relationship to someone like Thatcher. The hubris wasn’t in her to the degree that she thought she could just waltz in.” So in the end did Streep feel she was defending Margaret Thatcher in the film? “I don’t think she needs defending,” she says emphatically, her voice flashing a glint of Iron Lady conviction. “She owns her place in history, written in granite.” The same could be said for Meryl Streep.