On the first day of rehearsals for “Saving Mr. Banks,” Jason Schwartzman was running 20 minutes late. By the time he got to the tableread with Emma Thompson and the rest of the actors, he was in an apologetic frenzy. It got worse when Thompson, whom he had never met before, suddenly exploded.

“I just flew in from London!” she bellowed. “The least you could do was be on time!” An awkward hush fell over the room, and Schwartzman was horrified.

“Though my body was the same, within me I was shrinking,” says Schwartzman, who plays “Mary Poppins” songwriter Richard Sherman. “I was so embarrassed, and then she started laughing and the whole thing was a joke. The fear that she put in me, I used that for the rest of the shoot.”

While delivered in jest, the reprimand personifies Thompson’s dry wit and penchant for pushiness.

“My dad always thought I would be a director because I was so bossy,” says Thompson, who suffered a devastating blow when she lost her father, Eric Thompson, when he was just 53.

She briefly considered directing, but realized she had no interest. “Why would you?” she asks, in an erudite voice that sounds like a college literature professor’s. “It’s a horrible job. It’s so hard directing. My father was a director and I was married to a director (Kenneth Branagh).”

In many ways the role she landed in “Saving Mr. Banks” befits the British actress, comedian and writer: the uber-bossy author P.L. Travers, creator of “Mary Poppins,” who tortures Walt Disney (played by Tom Hanks) before eventually softening her stance and signing away the rights to her beloved literary character.

Thompson, too, had been feeling tortured creatively.

Despite having won Oscars for best actress (1992’s “Howards End”) and screenwriter (her adaptation of 1995’s “Sense and Sensibility”), and earning kudos for memorable turns in “The Remains of the Day,” “Nanny McPhee” and HBO movies “Wit” and “Angels in America,” both directed by Mike Nichols, Thompson has lately been largely relegated to supporting roles in films like “Beautiful Creatures,” “Men in Black 3” and the “Harry Potter” series. Her last starring role was in the 2010 sequel “Nanny McPhee Returns,” a box office disappointment.

“I hadn’t worked for a while, and I said to my agent, ‘I’ve got to earn some money,’ ” says the 54-year-old thesp. “I got offered, in quick succession, a very old lady in a wheelchair; Bradley Cooper’s mother (in ‘Silver Linings Playbook’); and Mother Teresa. And I thought people must assume I still look like Nanny McPhee,” in which she plays a British caretaker with a single scraggly tooth and a wart on her chin.

The “Nanny McPhee” movies are more similar in tone to Travers’ “Mary Poppins” book than the saccharine Disney movie ever was, suggests Lindsay Doran, Thompson’s longtime producing partner. Travers is a role that Thompson “was born to play,” Doran says. The multilayered part requires steeliness on the surface and vulnerability underneath.

Travers also lost her dad young. “I think when my father died, I swallowed him whole, and I think she did too,” Thompson says. “She swallowed a lot of pain, which she spent the rest of her life metabolizing.”

There wasn’t anything as sweet as a spoonful of sugar behind the scenes of “Mary Poppins,” and it’s this little-known backstory that provides the spine for “Saving Mr. Banks,” which bows in limited release Dec. 13.

In the movie, Travers battles Walt Disney after learning he wants to seize the rights to the book, her most prized creation. Even when she reluctantly agrees to leave London to spend two weeks in creative meetings at the Disney lot in Burbank, she lectures the crew and threatens not to sign the contract every time she doesn’t get her way.

Director John Lee Hancock (“The Blind Side”) says Thompson told him early on that Travers was the most difficult character she had ever played. “At every turn, she’s different than you think she’s going to be,” Hancock says. “At one point, she seems old and brittle, and at another point, she seems sensual.”

Disney studio chief Alan Horn says Thompson cleared a formidable hurdle in her portrayal. “It’s a very big challenge for an actress to be unlikable, and on the other hand be lovable,” he says. “And she did it.” Hanks, who plays Walt Disney in the film, says Thompson possessed the role from the start. “No one understands the process of translating a performance from a screenplay better than Emma,” he notes.

To capture Travers’ prickly exterior, Thompson did meticulous research. She studied Travers’ books, letters and photographs. The author didn’t trust Disney to keep his word about the adaptation, and had ordered all their business interactions be recorded — an artifact that still remains in the studio’s vault.

Those records proved an invaluable tool.

“You can tell so much about a person’s state of mind through the way they use their voice,” Thompson says. “Travers is always using hers to control them, to stop them; the voice is like a sword and shield. It’s all that she had.”

But Thompson couldn’t bring herself to listen to all the recordings. “It would have killed me,” she says. “It’s not a conversation. It’s a battle.”

An unforeseen battle in the making of “Saving Mr. Banks” had to do with Thompson’s hair for the role. In real life, Travers had a simple bubble cut with frilly curls. The hairdo matched her steely personality, and was a crucial foothold into the character. But Thompson is wig averse: “I think a lot of energy comes off the top of your head when you’re acting,” she says, “and a wig really puts the lid on it.” So she visited a salon to get the Travers cut. “I went in willingly like the proverbial woolly lamb to the slaughter and I came out looking like a baby woolly mammoth,” Thompson says. She wasn’t expecting her hair to feel so tight after her perm. She tried to unspool the curls, even going as far as rubbing olive oil on her scalp, but it was no use.

“I did everything I could,” Thompson says. “I rolled around. I pulled at it. I think the spirit of P.L. Travers was going, ‘If you’re going to play me, I’m going to make you suffer — you’re not going to have sex for months on end.’ ” Not wanting to be seen with Travers’ coif, Thompson spent much of her time on the Los Angeles shoot in a solitary space. One night in London, she met her pal, writer-director Richard Curtis (“Love Actually”), for dinner. She texted him with an advance warning: “Beware the hair.” She spent the rest of the evening teasing her husband, actor Greg Wise, about it. The gist of the joke, according to Curtis, was “they’d grow old happily together with her and the tight perm.”

It was worth the sacrifice. “Saving Mr. Banks” is garnering Thompson Oscar buzz for the first time in almost 20 years. “I’m praying that she gets nominated, for selfish reasons, because I’d love to play with her in the audience,” says her friend (and Oscar host) Ellen DeGeneres, who in 1997 featured Thompson in an episode of her former sitcom. “She deserves to be nominated, because she’s so brilliant. How often does a role come up to play a 54-year-old woman like that?”

Thompson recalls being around 7 when she first saw “Mary Poppins,” but has no memory of the actual theatrical experience. She just remembers how she felt. “I was profoundly moved by the songs,” the actress says. “ ‘Feed the Birds’ made me infinitely sad and melancholy as a child. ‘Let’s Go Fly a Kite’ made me cry. There’s something about those songs. It’s Mozartian. It’s like you feel those chords came out of the Big Bang.”

Of course, if Travers had managed to have her way, there would have been no singing in “Mary Poppins.” She opposed the idea of a musical.

“She was terrible,” says Richard Sherman, who co-wrote the songs in the film with his brother Robert. “The first thing she said was, ‘I don’t even know why I’m talking to you gentlemen, because we’re not going to have music in this film.’ She was a hurt little girl, and she never forgot it. She carried it with her all her life.”

Travers, who died in 1996, led a colorful life that included a failed career as an actress, purported bisexual relationships and an adopted son (none of which is mentioned in “Saving Mr. Banks”). Nobody in Hollywood seemed interested in telling Travers’ story on the bigscreen until producer Alison Owen at Ruby Films suggested honing in on the Disney subplot. When the project came across the desk of screenwriter Kelly Marcel (“Fifty Shades of Grey”), she was instructed to focus solely on Travers’ connection to the production of “Mary Poppins.” She included many lines from the Disney film, as well as its songs and a scene set at Disneyland with Walt and Travers riding the carousel together.

It was only later that Marcel realized the risk involved in doing that. “I was so naive when I started writing it,” she says, admittedly oblivious that Disney owned the intellectual rights to the material. “Once I finished it, I was like, ‘Oh shit. There is only one studio who can make this film, and they’ll probably give us a cease-and-desist order.’ ”

Horn doesn’t believe any other studio could have made “Saving Mr. Banks.” “Why would Paramount make a movie about Walt Disney?” he asks. “I think that would be a difficult pitch.”

It was also a difficult pitch to Disney, which had never made a movie that featured its founder. If it veered too far in one direction, the film could have seemed like a self-promotional infomercial. Too far in another, and it’s an embarrassing blow to the brand.

After landing on the Black List in 2011, the script for “Saving Mr. Banks” made its way to the desks of Disney executives. Production president Sean Bailey says his team was impressed by just how good the story was.

“We thought through every option,” Bailey says. “We thought, Do we buy it and shelve it? Or do we buy it and go for it?”

With no studio chief in place at the time (Rich Ross had been fired and Horn had not yet been hired), the latter option was only possible with a sign-off from Walt Disney Co. chief executive Bob Iger. “We knew if we wanted to put Walt onscreen, it needed to be a conversation Bob would be part of,” Bailey says. Once Iger approved, Marcel was granted access to all the Disney archives, including Travers’ tapes. She livened up some scenes to include real exchanges between the “Mary Poppins” writer and the befuddled Disney crew — like one nasty fight over how the Banks house looked too glamorous.

Hancock, who, like Travers, wasn’t sure he wanted to make a film with musical numbers, was also seduced by the quality of the script. He says his first and only choice for the role of the truculent author was Thompson.

“Emma is such a confident actor that there are times with just a look, she gives a soliloquy,” he says.

She’s had special training when it’s come to that. “I was doing a mime course in Paris with a great French clown who I learned a lot from,” says Thompson, who was 24 at the time. “At bottom, I am a clown.”

Thompson wanted to be a comedian like Lily Tomlin when she grew up. “That was my dream,” she says. At Cambridge, she joined the Footlights troop of sketch comedians, along with Stephen Fry and Hugh Laurie. After a few years, she starred in her own comedy show in England, which featured her mom (actress Phyllida Law) and Branagh, her boyfriend at the time. The critics ripped it to shreds, and she stopped writing — until Doran, who saw the show, tapped her to pen the script of “Sense and Sensibility,” which she had set up with Columbia Pictures movie boss Amy Pascal. Approached with the assignment, Thompson had a different Jane Austen request: “Couldn’t we do ‘Persuasion’ instead?” she asked.

“The first stage direction of ‘Sense and Sensibility’ had the word ‘susurrate’ in it,” Doran says. “I told her (Thompson) I’m a little worried that an American studio executive might not know what that means.” Thompson, an avid reader, shot back: “‘If they don’t know, they can look it up.’”

Mike Nichols, who has directed Thompson in three films, says Thompson’s sense of humor is impeccable. “All the best British actors start as comedians,” he explains. “To be able to be funny in character is the essence of acting. She writes the shit out of things. Her ‘Sense and Sensibility’ is a masterpiece.”

Thompson’s comedic flair burned brightly on Nichol’s “Primary Colors,” the political drama inspired (or not) by Bill and Hillary Clinton. When she ran into former president Clinton at Nelson Mandela’s 90th birthday in 2008, she discovered that not everyone appreciated the role.

“He said, ‘We feel so much the same about so many things, but you did that horrible movie.’ And I’d completely forgotten. I said, ‘Which horrible movie?’ I thought he’d seen something that he hated.” She tried to get the president to understand what she had been doing. “I said, ‘Bill, did you ever see it?’ He said, ‘Of course not.’ I said, ‘Listen, the movie was about the press.'”

Even though she’s made movies since the ’80s, Thompson has never had the desire to move to Hollywood. She lives in London on the same block as her mother, where she’s raised her two kids. “I love coming to California and I love coming to Hollywood,” she says. “I’ve always been so warmly welcomed.”

Thompson recalls winning her first Oscar, a leading actress statue for “Howards End,” at age 33. While she called receiving the award onstage “extraordinary,” she enjoyed the aftermath backstage even more — “that feeling all the crew were so lovely to me because I was a foreign lady they never heard of.”

When she returned to her hotel room with her mom — “Merchant Ivory didn’t have very much money,” she explains — flowers and balloons and gifts started to arrive. “We really didn’t have room to move,” she says (ironically, reminiscent of a scene in “Saving Mr. Banks” in which Disney inundates Travers’ hotel suite with company merchandise). “We were sitting in our dressing gowns. It was like a mortuary. It was just flowers everywhere. I honestly think you could have laid us out and put our hands like this and you have two dead people in a chapel of rest.”

Thompson keeps her two Oscars in the downstairs bathroom in her London home so that guests can see them. “I had them redipped,” she says. “I sent them over to America, and they came back all sparkly.”

On the day of her interview with Variety, Thompson, too, was about to be dipped — well, her hands and feet anyway, in cement, at Grauman’s Chinese Theater. She wasn’t sure what the ceremony would entail. “Perhaps they’ll just throw me in the L.A. River afterwards, which won’t matter of course, because it’s just six inches deep,” she says. “I’ll just lie there looking at the stars, thinking, ‘At last, I’ve arrived.’ ”