The action takes place in and around the Banks' household somewhere in London at the turn of the last century.
The show opens with Bert, a man of many professions and a good deal of mystery, introducing us to Cherry Tree Lane (Chim Chim Cher-ee/Cherry Tree Lane). At number 17, the Banks family may be found - Mr and Mrs Banks, their two children, Jane and Michael and their cook, Mrs Brill together with an odd-job man, Robertson Ay.
Things at 17 Cherry Tree Lane are not going well. Jane and Michael are out of control and, unsurprisingly, they get through nannies at a frightening rate. As the show starts, we see the last one, Katie Nanna, storm out and so it is time to find another. Taking matters into their own hands, the children decide to write the advertisement (The Perfect Nanny).
Dismissing their ideas, Mr Banks tears up the piece of paper and throws it on the fire, not seeing that a gust of wind has taken it up the chimney. Within moments a nanny, fitting the children's requirements exactly, arrives. Her name of course is Mary Poppins and she quickly demonstrates that she is more than a match for the naughty children. In fact, she has every confidence in her own qualifications and merits (Practically Perfect).
Mary immediately takes control. No rudeness or disobedience is tolerated, but in return for the children's good behaviour she introduces them to a world of magic. On their first trip to the park, they meet Bert and, despite their reservations about his ragged clothes and dirty face, Mary teaches them that they must learn to look past appearances; that beneath the ordinary surface of life, they might make wonderful discoveries if they will only look. To illustrate the point, Mary and Bert transform the park statues who come to life and dance with them (Jolly Holiday).
But, while Mary may be managing the children, it is clear that the real problem at number 17 lies at the heart of the family. Winifred Banks is aware that she is somehow disappointing both her children and her husband (Being Mrs Banks) and she doesn't seem able to communicate with any of them. George Banks, on the other hand, can't understand why she finds the role of wife and mother so difficult. In an effort to please him, Winifred sends out invitations for a smart tea party, (A Spoonful of Sugar) but when her plans go wrong she feels more lost and downhearted than ever.
Mary takes the children to visit their father at the bank where he works (Precision and Order). Furious about the intrusion into his working day, Mr Banks sends them away; although an innocent question asked by Jane makes him realise how much his values have changed (A Man Has Dreams) since he was an ambitious, idealistic, young man.
Outside St Paul's Cathedral, Mary introduces the children to the Bird Woman. Jane is suspicious of her, but Michael has already learned from Mary that he must look past appearances (Feed the Birds). On the trip home, the children meet the enigmatic Mrs Corry, a woman as old as time itself, who runs a magic sweet shop that also sells words (Supercalifragilisticexpialidocious). As Mary Poppins and the children enjoy their carefree adventures, things start to go wrong for their father when a risky business decision at the bank appears to have disastrous consequences. Winifred offers her support, but she is given short shrift by her angry and frustrated husband. The children return home full of fun, but their father explodes with rage and sends them to their room.
Reacting to her father's outburst, Jane flies into a fury, ignoring Mary Poppins' words of warning about controlling her temper. The frightening consequence of her anger becomes apparent as her toys take on a life of their own and teach the naughty children a lesson they will never forget (Temper, Temper). This song has been replaced with (Playing the Game).
Realising that Jane and Michael still have a lot to learn, Mary decides to leave Cherry Tree Lane (Chim Chim Cher-ee (Reprise)), to bring them to their senses. Her distraught charges find a note bidding them 'au revoir', which they soon learn means that perhaps they will meet Mary Poppins again...
In a misguided attempt to please her husband, Mrs Banks arranges for his former nanny, Miss Andrew, to take over from the suddenly departed Mary (Cherry Tree Lane (Reprise)). Whilst Mary Poppins may be disciplined, Miss Andrew is a brutal tyrant, rejecting any notion of a 'spoonful of sugar' in favour of her own terrible elixir (Brimstone and Treacle).
Terrified of their new nanny, the children escape to the park and into the arms of their good friend Bert, who cheers them up and helps Michael fulfill his dream of flying a kite (Let's Go Fly a Kite). Then, suddenly, floating down from the skies holding on to the kite string, Mary Poppins returns. She knows that this time the children will listen to her. She wastes no time in confronting the formidable new nanny, and an epic battle ends with Miss Andrew returning whence she came.
After also hiding in the park from Miss Andrew (Good For Nothing), George returns home. To his relief he finds Mary Poppins there instead. Not only has peace returned to the house, but Winifred at last understands her husband and the damage that was done to him as a boy. She can face the challenge ahead because her confidence has come back to help her fight for him (Being Mrs Banks (Reprise)). On their next adventure, Bert introduces the children to his friends the chimney sweeps (Step In Time). Jane and Michael learn that the sweeps are their guardians and will always be there in times of need.
It is time for Mr Banks to face up to the crisis he has caused at the bank. Bert helps him to remember his childhood and allows him to reflect upon the man he has become. Shaking Bert's hand for good luck (A Man Has Dreams/ A Spoonful of Sugar (Reprise)), George prepares to meet the Chairman of the Bank and accept his dismissal.
Winifred tells the children how she would like to have gone with their father, but he has forbidden it. The children encourage her not to accept barriers in life but rather to do what she thinks is right (Anything Can Happen If You Let It). Winifred hurries away while Mary teaches Jane and Michael their final lesson, taking them with her up to the heavens, where they meet the lamplighters, who fill the sky with stars. Still under cover of the song, they are invisible witnesses to their father's fate.
At the bank, George is shocked to learn the truth about his choice: far from ruining the bank, as he had thought, he has made a fortune. The Chairman is delighted. Winifred, arriving to defend her husband, finds instead he is the hero of the hour. George apologises for underestimating her, and together they return to the house. They are a united family now and ready to face a brighter future together.
Mary realises that her task is now done. With regret she says goodbye to Bert and sets off to bring magic into the life of another family (A Spoonful of Sugar (Reprise)).
Michael is delighted with the kite his father has made for him, Jane has the locket Mary has given her and the two children watch as their parents waltz happily together.
Then they all wish upon a shooting star - a star that we recognise as a dear, familiar figure who soars overhead on her way to her next adventure...