As American movie theatres go, the Paris, the tiny one-screen art-house that graces a corner of Fifth Avenue in New York adjacent to the storied Plaza Hotel, is usually a haven of understated elegance and manners. Home, customarily, to avant-garde European films with an audience size that most Hollywood producers would sniff at, the cinema opened by Marlene Dietrich in 1948 is not the sort of place where punters squabble over available seats. But at a special BAFTA screening of The Iron Lady recently, just ahead of its New York premiere, it became the scene of a rather undignified scramble, as a determined crowd jostled to snatch up precious tickets before the hordes of hopefuls hanging around “on the waiting list” nabbed them. The reason for this stampede? Meryl Streep, fresh off a plane from China, was in attendance, and would be giving an interview and Q&A session after the screening. For the British-studded audience, which included the UK ambassador to the United Nations, it was a golden opportunity to hear how the actress felt about playing Margaret Thatcher; and, in light of sustained early criticism from the British right, to determine whether Phyllida Lloyd’s film was really the “intrusive, unfair” attack against Thatcher that is purported in certain quarters to be – or whether in fact it is a meditation on something altogether more compelling and profound: the distorting, discombobulating power of memory; the grief of something irredeemably lost; the possibility of reconciliation,with oneself or others.

Streep may be far from your average Hollywood actress, but she knows how to turn on the charm. Taking to the stage moments after the credits rolled she was quick to offer an apology. “I know that it was very presumptuous to go to England and be the American playing Margaret Thatcher,” she assured us (with needless humility; it is hardly the first time an American has assumed our juiciest roles.) “But there are elements of all the characters I’ve played inside me. I don’t think I’m that different from elements of her. I tried to swallow her whole.” In any case, Streep believes that “one of the things that made Thatcher Thatcher was her position as an outsider”. This, after all, was the Grantham grocer’s daughter who become one of a handful of women in parliament; then the first female leader of a political party in the UK or any other major Western democracy; and later the only female Prime Minister we’ve ever had. If such a life seems incomparable to that of a feted Hollywood star, Streep likes to remind people that she was once one of the first female students at an all-male college. “Where we were excluded from many things because of, you know, our limited intellectual capacity,” she said.

As conversation turned, inevitably, to the preparation she did for the role, much of which takes place in Thatcher’s late life, Streep unwittingly confirmed the suspicion that her talent is instinctive by confessing that she “usually doesn’t prepare much”. For Maggie, though, she told us she’d intended to give herself four whole months to get the hang of her. “But stuff happened.” Her husband got sick; she arrived in London a mere fortnight before shooting began – just enough time to go “backstage” at the House of Commons, where she was struck by “how intimate and tiny” Parliament felt. (“I wish they had PMQs in this country,” she added, to which the New Yorker seated next to me responded, reverently, “Amen.”) By her own admission, Streep hadn’t known too much about Thatcher before she was offered the role. “I wasn’t interested until I was interested,” she said. “I had a barebones understanding of her friendship with Reagan. I thought she dressed badly (so did I but that didn’t matter). I thought it was great that Britain had admitted a female Prime Minister and foolishly assumed that it would happen here in the US in a minute.” By chance, she had once seen the former PM speak at her daughter’s university – and she told a funny anecdote about how their paths nearly crossed by coincidence during shooting. “The ‘Streepers’ – that’s my little group of fans; I think we have Mamma Mia to blame – turned up while we were shooting a scene in Battersea Park,” she recalled. “They got bored with hanging around and went for a walk, where they came upon Maggie Thatcher. They asked if she was here for the shooting. She looked confused. The minder, when told what it was, remarked, ‘Oh, I think that’s one we won’t be watching.”’ But besides that accidental research, she’d had precious little time to prepare to become one of the most recognisable women in history.

“I got on a plane and I had not ‘done’ her,” she recalled. “So day one was a bit not great, but there were all these splendid English actors at Pinewood and you’ve got to love other actors; they gave me my belief. And you really have to believe, right to the soles of your feet.” By day two, they were filming a major scene when Thatcher excoriates Geoffrey Howe, and Streep’s feet were apparently still unconvinced. “I was so freaked out,” she confessed. “But sometimes a bath of fire is good; when it’s terrifying and hard and ridiculous – that’s good.” The twice Oscar-winner who has been nominated for more Academy Awards and Golden Globes than any other actor is such a consummate artist that it’s hard to imagine she finds anything terrifying, hard or ridiculous. But she was eager to disabuse us of this assumption. “Sometimes I got hysterical and lost my mind and thought, ‘I don’t think I can do this.’ Phyllida would say, ‘Yes you can’.” Praising her director for being “smart, truthful, organised, no bullshit”, Streep added that “it’s good to be nervous, insecure; that’s a very good thing”. Then, with a wry smile, she corrects herself. “I mean, it’s horrible, but it’s the thing that enables you to understand weakness. And often you need to know what that is.”

The question of weakness is at the heart of Lloyd’s film, which takes as its central premise an observation made by Carol Thatcher, in her memoir A Swim-On Part in the Goldfish Bowl, that her mother was struggling with dementia and sometimes had to be reminded that her husband, Sir Denis, had died. The Iron Lady has been lambasted by certain Tory MPs, including Rob Wilson, a parliamentary private secretary to Jeremy Hunt, who has called for a Commons debate about the film. ‘”But it’s not a biopic,” Streep insisted. “We’re looking at the end of a big, important life. It’s about the things that are drawn by memory; the dreaming at the end of a life. She and Denis upended the natural order of things: they had a very strong marriage, and she did depend on him. In Carol’s book she does say she forgets he’s not there. That touched me.” Not that Streep, an avowed Democrat (with a famously strong marriage) who has publicly criticised George W. Bush, is blinkered about the complex controversies enshrined in the name “Thatcher”. She had, she said, watched archival footage of “the great upheaval triggered by Thatcher’s politics” and was all too aware of the “venom” felt towards her by so many. “But I see the pain and devastation, and I think she did it from conviction,” she maintained. “Her decisions were based on something felt.” Moreover, Streep argued, the film explores with great poignancy the idea of “regret, of re-examination; of revisiting old places, old wounds. And we wouldn’t be human without that.”

Perhaps it was necessary for an “outsider” to take on this role in order that it might transcend the vexed political dimensions of Thatcher within the British consciousness and pose bigger human questions. “We all enter the dark corridor,” Streep reminded us. “What do you meet there? What interests me is forgiveness. How you forgive yourself and other people. How you reconcile yourself to choices that you’ve taken and the effects they’ve had on a life.” She paused, shook her head, almost imperceptibly. “Forgiveness. It’s the greatest thing human beings ever invented.”

‘The Iron Lady’ is released on 6 January