Meryl Streep shuffles down a London street wearing a kerchief, a drab beige overcoat and enough prosthetic wrinkles to pass as an octogenarian in the opening scene of her new movie about former British Prime Minister Margaret Thatcher, “The Iron Lady.” For Streep, shooting the sequence provided a jarring taste of a specific kind of invisibility. “There is no more dismissible figure on the street than an old woman,” Streep said over a mid-December lunch with her “Iron Lady” director, Phyllida Lloyd, in a cavernous suite at New York’s Waldorf-Astoria hotel. “I would search for people’s eyes, and I would look people full in the face, and they would assiduously avert their gaze. It was really interesting. You represent everything that is terrifying.” At 62, Streep is as visible as she’s ever been in her more than 30-year movie career — “The Iron Lady,” which opens in Los Angeles on Friday, looks likely to earn her a record 17th Oscar nomination for acting; President Obama, Secretary of State Hillary Rodham Clinton and Clint Eastwood just feted the actress at the Kennedy Center in Washington, D.C.; she even appears, wind-swept and rosy-cheeked, on the front of January’s issue of Vogue, the oldest cover subject in the fashion magazine’s history.

“The Iron Lady” is Streep’s second pairing with Lloyd: The 54-year-old British theater director’s first film was the 2008 musical “Mamma Mia!,” which grossed $600 million worldwide and is Streep’s biggest box office hit. Star and director are a study in contrasting temperaments: Streep is warm, breezy and quick to laugh — “There you go, babe,” she says, slicing a piece of red velvet cake to share. “Another day in the Waldorf Towers. Somebody’s gotta do it.” Lloyd is reserved, with a dry wit and a keen understanding of her leading lady’s needs — each day on set as Streep’s age makeup was removed, the director hand-delivered her a British delicacy: a cold, canned gin and tonic. “The Iron Lady” unfolds as a series of reminiscences by the aging Thatcher as she attempts to sort the belongings of her deceased husband, Denis (Jim Broadbent). Welsh newcomer Alexandra Roach plays Thatcher as the young Margaret Roberts — a grocer’s daughter with political aspirations that are audacious both for her class and her gender. Streep picks up the role for the last 40 years, as Thatcher rises in England’s Conservative Party, raises twins, becomes the first woman elected head of a government in the West and presides over a series of divisive policy decisions, including privatizing Britain’s public utilities, adopting a hard line against hunger-striking members of the Irish Republican Army and forging a strong alliance with President Ronald Reagan. A 2008 memoir by Thatcher’s daughter, Carol, “A Swim-On Part in the Goldfish Bowl,” helped inspire “The Iron Lady’s” partly fictionalized screenplay by Abi Morgan. In 2009, Morgan sent her script to Lloyd and European production company Pathé, where casting discussions quickly turned to Streep. Lloyd says she initially worried that casting an American actress might inflame British audiences but was convinced by a key quality that Streep and the former prime minister share: “Thatcher was extremely charismatic,” Lloyd says. “We needed someone who could match her charm.”

Much of the movie’s action unfolds through the use of news footage from Thatcher’s tenure in the 1980s, a period of economic hardship, civil unrest and terrorist attacks, all of which may feel remarkably current to American audiences living through the financial crisis, Occupy Wall Street protests and the fight against Al Qaeda. Carol Thatcher’s book was criticized by many of her mothers’ contemporaries for revealing details of the once-powerful leader’s encroaching dementia, a critique that also dogged the film after early screenings for some of Thatcher’s inner circle in Britain in August. “I didn’t come here to see a film about granny going mad,” one anonymous attendee told the British newspaper the Daily Mail, while the Daily Telegraph called the movie “disgraceful.” Capturing a life in its wane, however, was precisely what had interested Streep, and subsequent reviews from film critics have largely praised her portrayal of Thatcher both at the confident peak of her potency and during her vulnerable decline. “We’ve come under fire for trespassing on an old lady’s fragility,” Streep said. “In England, people say, ‘Oh, it’s shameful when she can’t defend herself.’ Defend herself from what? That someone is less of a human being because they’ve reached the end of their lives when things unravel?… I got very angry when I heard that criticism, that we can’t touch this because that should be behind closed doors. No, honestly, that’s life.”

“The Iron Lady” will be released in Britain on Jan. 6. Now 86 and house-bound after a series of strokes, Thatcher is still a political lightning rod there, more than 20 years after she resigned from office. “I’ve had cameramen who refused to work on the film,” Lloyd said. “People who’ve come up to me and said, ‘You’re putting me in a difficult position here because my mates, we saved up money to have a party the day she dies.’ … So the fact of this film is a provocation in England.” “The Iron Lady” was shot early this year at various locations in England, including Parliament and Pinewood Studios, for $14 million. (“‘Hugo Cabret’ was $170 [million],” Streep said of Martin Scorsese’s latest film. “You could make 10 Margaret Thatcher movies and have some left over for publicity!”)

In preparation, Streep and Lloyd met with members of Thatcher’s cadre as well as her onetime rivals. “We asked one of her key ministers, ‘If we were to capture one thing in this movie, what should we look for?’ And he said her loneliness,” said Lloyd. “He said the job is lonely enough, but compounded by her being such an outsider in a party, never going to the dinner parties, but also her belief that she always had to work 10 times harder than the men. She was always there first, she always left last. You just had this image of her alone at her desk, then everyone else is gone.” While trying to master Thatcher’s distinctive speaking style, Streep recorded voice memos on her iPhone patterned after a six-minute 1987 interview Thatcher had given to BBC journalist Robin Day. “She had prodigious reserves of breath,” Streep said, straightening in her chair and beginning to demonstrate Thatcherite respiration. “In drama school, they taught us that if you want to convey Marlowe’s mighty line or the meaning of a sonnet, you should practice doing it on one breath, because if you stay on one breath, the audience will stay with the thought you’re trying to convey, and if you keep going with it all the way to the end of your breath, they will get it” — Streep gasps. “She did that. It was astonishing. I couldn’t do it. I couldn’t match her breath for breath.”

To physically inhabit Thatcher, Streep donned her Aqua Net halo, shoulder-padded suits and ubiquitous pearls, all necessary tools, the actress says, in the leader’s political arsenal. “We do judge each other based on the way we look, and certainly, women are much more held to account on that score,” she said. Wearing an unfussy red shirtdress and some woven bracelets, Streep costumes herself more like the Connecticut wife and mother of four she is than a movie star. “We’ll take all sorts of dishevelment from men and accept it as darling eccentricity, but women can’t afford that. Churchill could cry once a week, but you can’t accept tears from a female president or prime minister because it would be seen as a sign of weakness. It’s just a different set of standards.” Female directors aren’t as unusual as female political leaders, but they’re still a relative rarity as are some of the other pivotal behind-the-scenes roles held by women on “The Iron Lady,” including screenwriter Morgan and editor Justine Wright.

“You have an understanding as a female director of the territory of transgression,” Streep said. “The crews in England, it is largely a man’s world still.” Even after “Mamma Mia!” became the highest-grossing British film at that nation’s box office, Lloyd, who has directed productions at the Royal National Theatre and the West End, said she tread carefully with crews. “The stakes feel very high still,” Lloyd says. “I have to not be shrieky on a film set. You have to know that you are still …” “… Provisional,” Streep finishes the sentence.

In contrast, Streep brings up the workmanlike brusqueness of Eastwood, who directed her in “The Bridges of Madison County.” “I remember Clint could say, ‘Pick that up and pull it over there. C’mon, I need it now!’ That’s one thing from a male voice. But from you, somebody’s [testicles] have just been cut off. It’s just too painful.” Streep and Lloyd seem vaguely horrified by American reporters comparing Thatcher with Republican presidential candidate Michele Bachmann, who is much further to the right on social issues than Thatcher ever was. “[Thatcher] would be appalled by the hijacking of conservatism in this country,” Streep said. “And yet she definitely was a fiscal conservative. She’s a brand of Republican that doesn’t exist anymore, is not allowed to exist.” In Streep’s long, chameleonlike career, from Holocaust survivor (“Sophie’s Choice,” 1982) to Danish baroness (“Out of Africa,” 1985) to television chef (“Julie & Julia,” 2009), there is only one role, she says, that men have ever told her they’ve connected with — her performance as a formidable fashion editor in “The Devil Wears Prada.” “The hardest thing for a male audience member is to put himself into the shoes of a female protagonist,” Streep said. “[In ‘Prada’], I had a position of leadership and responsibility and was beset by different quarters…. Men identified with that, the first time in, what, 30 years, that a man has ever said, ‘I knew how you felt.’ It reflects the role and maybe the larger culture, that we are acclimating to the idea that we can imagine women in these leadership positions. That’s why I think this movie might be very interesting to a male audience, because this woman lived a life that was previously within a male domain.”

“We feel we’re carrying a torch for all kinds of things that are not necessarily explicitly the biography of Margaret Thatcher,” said Lloyd. “It’s not a political film, except it’s political in wanting to put an old lady at the center of it.” “Yeah, that is a political act,” Streep agreed. “That is the most subversive thing you’ve done.”