Act I
Bert, a man of many professions, introduces the audience to Cherry Tree Lane ("Chim Chim Cher-ee/Cherry Tree Lane - Part 1") in Edwardian London. Number 17 is where the Banks family lives: George and Winifred Banks, their two naughty children Jane and Michael, their cook/maid, Mrs. Brill and their house boy, Robertson Ay. Things are not going well for Jane and Michael. They are out of control and, as the show starts, their latest nanny, Katie Nanna, storms out. After that, Mrs. Brill and Robertson Ay complain about living in a "madhouse." The children decide to write the advertisement for a new nanny ("The Perfect Nanny"), but George, having a very different idea of what constitutes the perfect nanny, tears up the piece of paper and throws it in the fireplace. The family all reflect on if they will ever find the perfect nanny ("Cherry Tree Lane - Part 2"). Within moments, Mary Poppins arrives, restored advertisement in hand, and takes charge of the Banks children, having every confidence in her own qualifications and merits ("Practically Perfect").

On the children's first outing to the park, they meet Bert and, despite their reservations, Mary teaches them that they must learn to look past appearances. To illustrate the point, Mary brings the park statues, including a mythological figure named Neleus, to life ("Jolly Holiday"). A storm starts to brew and the children quickly hurry home, but not before Neleus mentions how much he misses his father.

While Mary manages the children, other problems lie with their parents. Winifred is aware that she is somehow disappointing both her children and her husband. George, on the other hand, can't understand why she finds the role of wife and mother so difficult. In an effort to please her husband, Winifred sends out invitations for a smart tea party ("Cherry Tree Lane (Reprise) / Being Mrs. Banks / Jolly Holiday (Reprise)"). Mrs. Brill makes the preparations, while telling an eager Robertson Ay to keep his hands off. The children inadvertently sabotage the kitchen preparations, but Mary sorts it out with a lesson ("A Spoonful of Sugar"). However, it is then revealed that none of the invitees are coming and Winifred reflects on her failure at pleasing George ("A Spoonful Of Sugar (Reprise)").

Mary takes the children to visit their father at the bank where he works ("Precision and Order"). There, George is busy dealing with possible investment clients: firstly, an ambitious man named Herr Von Hussler with an elaborate money-making scheme, and then a middle-class man named John Northbrook with a simple factory project. George is furious when Mary turns up with the children, but an innocent question asked by Jane (What's more important, a good man or a good idea?) makes him realise how much his values have changed ("A Man Has Dreams") since he was an idealistic young man. He then decides to accept Northbrook's project and rejects Von Hussler's, even though he knows the bank disapproves.

Outside St. Paul's Cathedral, Mary introduces the children to the Bird Woman ("Feed the Birds"). Jane is suspicious of her, but Michael responds to the Bird Woman and throws crumbs for the birds. On the trip home, the children meet the enigmatic Mrs. Corry who runs a magic sweet shop that also sells words ("Supercalifragilisticexpialidocious").

The children return home in high spirits, unaware that things have gone wrong for their father. Unknown to them, George's decision to reject Von Hussler has cost the bank dearly, and he is suspended without pay. George explodes with rage at the children and they are sent to the nursery. Reacting to their father's outburst, Mary briefly points out that other members of the family are rarely there to take care of the parents, before Jane and Michael get into a fight over Jane's doll Valentine, prompting a displeased Mary to order them to bed and enchant them to sleep. The frightening consequence of Jane's anger becomes apparent moments afterwards, as Valentine and the rest of Jane and Michael's disgruntled toys come to life and join Mary in teaching them a lesson in how to take better care of their belongings and toys (formerly "Temper, Temper", now "Playing the Game").

Believing that Jane and Michael need personal growth, Mary decides to leave Cherry Tree Lane ("Chim Chim Chimr-ee – Rooftop Duet"), to bring them to their senses. Her distraught charges find a note saying that perhaps they will see Mary again eventually. Jane and Michael wake up to find Mary Poppins and their toys gone, leaving only a note on the floor. It reads "Dear Jane and Michael, keep playing the game. Au Revoir, Mary Poppins." Mrs. Brill sees them awake and when asked about what Au Revoir means, she tells them that it means "Till we meet again." She sends them in for bed.

Act II
In a misguided attempt to please her husband, Winifred arranges for his childhood nanny, Miss Andrew, to take over from the suddenly departed Mary ("Cherry Tree Lane (Reprise)"). At the sight of her, a terrified George flees, exclaiming "the Holy Terror!" To everyone's shock and dismay, he is right. Miss Andrew is a brutal and cruel tyrant, quick to administer her own terrible elixir ("Brimstone and Treacle Part 1") and discipline by threatening to split Jane and Michael up by taking charge of Jane and sending Michael to boarding school. After Miss Andrew goes to her room, Jane and Michael decide that running away is the only solution.

The children find their good friend Bert, who cheers them up and helps Michael fulfill his dream of flying a kite ("Let's Go Fly a Kite"). Mary Poppins flies in on the kite from the sky and reunites with the children. They update her on Miss Andrew and she takes them home, planning to "surprise" Andrews.

Also hiding in the park is George, who is depressed over his supposed lack of achievements ("Good For Nothing"). Searching for him is Winifred, who at last understands her husband and the damage that was done to him by Miss Andrew ("Being Mrs Banks (Reprise)").

When the children return to Number 17, Mary sets Caruso, Miss Andrew's lark, free from his cage. This leads to a confrontation between the two nannies, ending with Miss Andrew having a taste of her own medicine as she is trapped in a large birdcage and vanishes down below ("Brimstone and Treacle Part 2"). Winifred and then George return at this point, surprised but pleased that Miss Andrew has "left".

The group ascends to the rooftops, where Bert introduces the children to his friends the chimney sweeps ("Step in Time"). The sweeps' dance eventually enters the house, causing chaos. As the sweeps quickly exit, George receives a telegram from the bank requesting his presence there. George assumes that he has been fired and decides it's time to sell the family heirloom. However, the vase is shattered accidentally by Mrs. Brill, who goes into a despairing shock since she had been cleaning it from the top of the shelf. When she is being led away for comfort, George goes to clean the broken pile himself, to find it reveal a collection of gingerbread stars from his childhood. This leads to a brief moment of reflection for George ("A Man Has Dreams (Reprise) / A Spoonful Of Sugar (Reprise)"). After shaking hands with Bert, George leaves to meet the Chairman of the Bank.

At the children's encouragement, Winifred decides to follow her heart and be at George's side at the bank ("Anything Can Happen (Part 1)"). Unseen to anyone else, Mary takes Jane and Michael into the sky to follow, where they watch the unfolding events. On his way to the bank, George encounters the bird woman and gives her tuppence to feed the birds ("Feed The Birds (Reprise)")

At the bank ("Precision And Order (Reprise)"), George is surprised to learn the consequence of his choice: far from ruining the bank, he has made a fortune by both rejecting Von Hussler and approving Mr. Northbrook's loan. They ask for the word that made them so successful, which George admits to be Mary's word, ("Supercalifragilisticexpialidocious (Reprise)"). Winifred, arriving to defend her husband, finds instead he is the hero of the hour. After she mentions Miss Andrew's name to the Bank Manager, the old man too relates his experience under "the Holy Terror". Winifred convinces the manager to quadruple George's salary. George apologizes for underestimating her, and together they return to the house. Mary and Bert take the children across the skies and they see everyone they met along their journey including Mrs. Correy, Neleus, and even Miss Andrews, who kindly shakes hands with Michael ("Anything Can Happen (Part 2)").

Mary realises that with the family reunited and happy, her task is done. With regret, she says goodbye to Bert with a kiss on the cheek and sets off (A Spoonful Of Sugar (A Task Is Done)"). Jane and Michael accept that Mary is leaving them and tell her that they'll never forget her. The two children watch as their parents waltz happily together and Mary flies high above the audience.