Glenn Close has just been crucified, and it sounds like it went rather well. A few days before we meet, the actress recorded her big show-stopping scene for a new musical in which her character, the protagonist's Scottish mother, nails herself to a cross.

"It's largely autobiographical," Close laughs. "Once my hands are both up there, John's character asks to be hugged, and I explain that I can't, because I've crucified myself."

Her only concern, at this point, is that her Glaswegian accent won't stand up to scrutiny: "I didn't really have time to perfect it," she frowns.

The musical, by John Cameron Mitchell, director of Hedwig and the Angry Inch, is called Anthem, and will be released next year as a serial podcast, the 71-year-old actress's first such credit in a career that has spanned the stage and screens of all sizes. In the cinema, she has been the bunny-boiling Alex Forrest in Fatal Attraction and the Dalmatian-skinning Cruella de Vil; on television, Patty Hewes in the legal drama Damages; on Broadway and in the West End, Norma Desmond in Andrew Lloyd Webber's Sunset Boulevard.

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Close was moving between mediums before it was cool, or even broadly possible: she recalls in 1982, after breaking into Hollywood via the oddball Robin Williams vehicle The World According to Garp, being offered the lead in a made-for-TV film called Something about Amelia - "and my agent said to me, 'This will ruin your movie career'."

When she began Damages, the actress Holly Hunter rang to ask how life was in the then-dawning age of prestige television. "And I told her it's fabulous. And then she did one too."

It is an overcast Thursday, with London veiled in drizzle for the British premiere of Close's new film, The Wife: no auto-crucifixion here, but much self-mutilation and sacrilege of a subtler type. Adapted from Meg Wolitzer's 2003 novel, it is a dark and devious character study in which Close plays Joan Castleman, the supportive spouse of the grey-maned literary lion Joe Castleman (Jonathan Pryce), who has been summoned to Stockholm to receive a long-anticipated Nobel Prize. Tagging along as his plus-one, Joan reflects with dismay, and then wrath, on a life spent in her husband's shadow - and in their hotel room, grievances are aired, secrets exhumed.

Set in the Nineties, with flashbacks to Joan's student days, it plays as a sly riposte to the so-called "Great Man theory" of history.

Close describes it as "part-period piece, part-love story, part-Bergmanesque drama - so much so the latter that it could have been called Scenes from a Marriage. I think it's good that it's hard to characterise. Kind of like life, right?"

Close's performance in Fatal Attraction led to her fourth of six Oscar nominations to date. And as soon as The Wife screened at last year's Toronto Film Festival, the talk began again: could this be the role that finally clinches it? With a politician's tact, she says she is "thrilled" by the speculation, particularly as she sees the part as "one of the trickiest I've had to play. Because I had to come up with an answer to a big question: why hasn't she left him? I was so sure that all the women in the audience would jump up and yell 'Just leave him!' So I had to answer that question for myself."

Doing so involved some searching conversations with her 30-year-old daughter Annie Starke, who plays the young Joan in flashback. "She had to establish who Joan is: my job was to follow her," Close says. "She's a millennial, as they say, and they were all born after feminism. I thought the character would be hard for her generation to understand. But she got it, she did her homework."

In preparing, the two talked about Close's own mother, the New England socialite Bettine Moore, who died aged 90 in 2015, "and totally deferred to my father our whole lives. She was a woman of great potential who, at the end of her life, tragically said, 'I feel like I've accomplished nothing'."

Close's father, William, served for 16 years as the personal physician of Mobutu Sese Seko, the dictatorial president of Zaire.

"My dad was brilliant, but it was all about him," says Close.

She and her siblings advised their mother to file for divorce.

"But she said, 'No, I made a vow' - they got married in 1944, you know, so it was a different world. But it was painful to watch.

"So I'd seen this story in my own family. My father ... always put himself in a position where the people he took care of worshipped him."

Off-screen, Close has been married three times; she divorced her third husband in 2015. The first, whom she wed at 21 and split from two years later, was a guitarist she met while singing with Up with People, the musical branch of Moral Re-Armament, the right-wing religious cult. Her family immersed themselves when Close was 7, leaving their Connecticut estate for the group's headquarters in Switzerland.

She only extracted herself in her early 20s, when she went to study drama and anthropology at college.

She has never spoken in detail about it, nor explained the mechanics of her breakaway, but plans to do so in a memoir, a contract for which she signed years ago, and "which I will write when I can stop working for long enough to clear the decks and really dig in. Because I think that whole dynamic is fascinating. And how to survive it is fascinating. And the damage it can do is relevant".

She visited a childhood trauma specialist "not too long ago - even at my age, which is kind of astounding. But it establishes these trigger points that affect you for the rest of your life. I think anybody who has gone through any kind of experience like that doesn't want to be affected by it, because it is a kind of PTSD. I think it really is interesting how deep it runs".

Close's fascination with brave faces and buried selves rings out clear in The Wife, just as it did in 2011's Albert Nobbs, which, like her new film, required 14 years of prodding and persuasion on her part to make. Early in her career, she starred in a stage adaptation of the original George Moore short story, about a woman living as a male butler in 19th-century Dublin.

The character never left her, so she secured the rights in the early '90s, and reprised the role almost three decades later.

Close, but no cigar: Her six Oscar nominations

The World According to Garp (1983): Close's screen debut at 35 was as the feminist mother of Robin Williams's struggling writer in this sexually charged picaresque.

The Big Chill (1984): Hollywood's love for Close was clear when nod two followed 12 months later, for her work in Lawrence Kasdan's comic drama about old college pals reunited.

The Natural (1985): Her third nomination in as many years came for her work as Robert Redford's childhood sweetheart in this sentimental baseball drama from Barry Levinson.

Fatal Attraction (1988): The inimitable Alex Forrest gave Close the first of her three Oscar duels to date with Meryl Streep. On the night, both lost to Cher in Moonstruck.

Dangerous Liaisons (1989): Playing the calculating Marquise de Merteuil for Stephen Frears pitted Close against Streep again, although Jodie Foster eventually came out on top.

Albert Nobbs (2012): A 23-year hiatus was broken by this odd but bold and deeply felt turn in Rodrigo García's gender-swapping period drama. This time, Streep as Thatcher triumphed.