The film, set in 1961, begins in London. Agent Diarmund Russell urges financially strapped author Pamela “P. L.” Travers to travel to Los Angeles and meet with Walt Disney. Disney has pursued the film rights to her Mary Poppins stories for twenty years, having promised his daughters to produce a film based on the books. Travers has steadfastly resisted Disney’s efforts, fearing what he will do to her character. Having written nothing new and her book royalties dried up, she risks losing her house. Russell reminds her that Disney has agreed to two major stipulations (no animation and unprecedented script approval) before she finally agrees to go.
Flashbacks depict Travers’ difficult childhood in Allora, Queensland, Australia, which became the inspiration for much of Mary Poppins. Travers idolized her loving, imaginative father, Travers Robert Goff, but his chronic alcoholism resulted in his repeated dismissals, strained her parents’ marriage, and caused her distressed mother’s attempted suicide. Goff died from tuberculosis when Travers was seven years old. Prior to his death, her mother’s stern, practical sister came to live with the family and later served as Travers’s main inspiration for the Mary Poppins character.
In Los Angeles, Travers is annoyed by what she perceives as the city’s unreality and the overly-familiar inhabitants, personified by her friendly limousine driver, Ralph. At the Walt Disney Studios in Burbank, Travers meets the creative team that are developing Mary Poppins for the screen: screenwriter Don DaGradi, and music composers Richard and Robert Sherman. She finds their presumptions and casual manners highly improper, a view that she also holds of the jocular Disney.
Travers’ working relationship with Disney and his team is difficult from the outset, with her insistence that Mary Poppins is the enemy of sentiment and whimsy. Disney and his people are puzzled by Travers’ disdain for fantasy, given the nature of the Mary Poppins story, as well as Travers’ own rich imagination. She particularly objects to how the character George Banks, the children’s estranged father, is depicted, insisting that he is neither cold nor cruel. Gradually, the team grasp how deeply personal the Mary Poppins stories are to Travers and how many of the characters were inspired by her past.
The team acknowledges that Travers has valid criticisms and make changes although she becomes increasingly disengaged as painful childhood memories resurface. Seeking to understand what troubles her, Disney invites Travers to Disneyland, which, along with her developing friendship with Ralph, the creative team’s revisions to the George Banks character, and the addition of a new song and a different ending, help dissolve Travers’ opposition. Her creativity reawakens, and she begins collaborating with the team. Soon afterward, however, Travers is enraged to discover an animation sequence has been added. She confronts Disney over his broken promise and returns home.
Disney learns that “P.L. Travers” is a pen name, taken from Travers’ father’s given name. Her real name is Helen Goff, and she is Australian, not English. That gives Disney new insight into Travers, and he follows her to London. Arriving unexpectedly at her home, Disney shares his own less-than-ideal childhood but stresses the healing value of his art. He urges Travers not to let deeply-rooted past disappointments dictate the present. That night, after Disney has left, Travers relents, granting the film rights.
Three years later, in 1964, Travers has begun writing another Mary Poppins story, while Mary Poppins is to have its world premiere at Grauman’s Chinese Theatre in Hollywood. Disney has not invited Travers, fearing how she might react with the press watching. Prompted by Russell, Travers shows up unannounced at Disney’s office; he reluctantly issues her an invitation. Initially, she watches Mary Poppins with a lack of enthusiasm, particularly during the animated sequences. She gradually warms to the rest of the film, however, becoming deeply moved by the depiction of George Banks’ personal crisis and redemption.