In Edwardian London, 1910, Bert entertains a crowd as a one-man band when he senses a change in the wind.
Afterwards, he directly addresses the audience, and gives them a tour of Cherry Tree Lane, stopping outside the Banks family's home. George Banks returns home to learn from his wife, Winifred, that Katie Nanna has left their service after their children, Jane and Michael, have run away, “For the fourth time this month,” ("Life I Lead"). They are returned shortly after by Constable Jones, who reveals the children were chasing a lost kite. The children ask their father to help build a better kite, but he dismisses them. Taking it upon himself to hire a new nanny, Mr. Banks advertises for a stern, no-nonsense nanny. To contrast, Jane and Michael present their own advertisement for a kinder, sweeter nanny. Mr. Banks rips up the letter, and throws the scraps in the fireplace, but the remains of the advertisement magically float up and out into the air.
The next day, a number of elderly, sour-faced nannies wait outside the Banks' home, but a strong gust of wind blows them away, and Jane and Michael witness a young nanny descending from the sky using her umbrella. Presenting herself to Mr. Banks, Mary Poppins calmly produces the children's restored advertisement, and agrees with its requests, but promises the astonished banker she will be firm with his children. As Mr. Banks puzzles over the advertisement's return, Mary Poppins hires herself, and she convinces him it was originally his idea. She meets the children and helps them magically tidy their nursery by snapping, before heading out for a walk in the park ("Spoonful of Sugar").
Outside, they meet Bert, working as a screever; Mary Poppins uses her magic to transport the group into one of his drawings. While the children ride on a carousel, Mary Poppins and Bert go on a leisurely stroll. Together, they sing ‘Jolly Holiday’, where Bert flirts with Mary Poppins. After the duo meets up with the children, Mary Poppins enchants the carousel horses; they rescue a fox from a fox hunt followed by a horse race which Mary wins. Describing her victory, Mary Poppins uses the nonsense word "Supercalifragilisticexpialidocious". The outing is ended when a thunderstorm dissolves Bert's drawings, returning the group to London.
The next day, the four meet odd Uncle Albert, who has floated up in the air due to his uncontrollable laughter; they join him for a tea party on the ceiling and tell jokes ("I Love to Laugh"). Afterward, Mr. Banks becomes annoyed by the household's cheery atmosphere, and he threatens to fire Mary Poppins, but she manipulates him into taking the children to his workplace, the bank, the next day ("British Nanny Reprise"). Mr. Banks does so, and the children meet Mr. Dawes Sr. and his son. Mr. Dawes aggressively urges Michael to invest his tuppence in the bank, ultimately snatching the coins from Michael. (Fidelity Fiduciary Bank) Michael demands them back; other customers overhear the conflict, and they all begin demanding their own money back, causing a bank run.
Jane and Michael flee the bank, getting lost in the East End until they run into Bert, now working as a chimney sweep, who escorts them home. The three and Mary Poppins venture onto the rooftops, where they have a song-and-dance number with other chimney sweeps, which spills out into the Banks' home ("Step in Time"). An enraged Mr. Banks returns and receives a phone call from his employers. He speaks with Bert, and Bert tells him he should spend more time with his children before they grow up ("A Man Has Dreams"). Jane and Michael give their father Michael's tuppence in the hope to make amends.
Mr. Banks walks through London to the bank, where he is given a humiliating cashiering and is dismissed. Looking to the tuppence for words, he blurts out "Supercalifragilisticexpialidocious!", tells a joke, and happily heads home. Dawes Sr. mulls over the joke and, finally understanding it, floats up into the air, laughing.
The next day, the wind changes, meaning Mary Poppins must leave. A happier Mr. Banks is found at home, having fixed his children's kite, and takes the family out to fly it. In the park, the Banks family meets Mr. Dawes Jr, who reveals his father died laughing from the joke ("Let‘s Go Fly a Kite"). Although initially sorry, Mr. Banks soon becomes happy for him, as Mr. Dawes Jr. had never seen his father happier in his life and re-employs Mr. Banks as a junior partner. With her work done, Mary Poppins flies away; Bert bids her farewell, telling her not to stay away too long.