“Mary Poppins is not for sale,” author P.L. Travers testily barks at Walt Disney. “I won’t have her turned into one of your silly cartoons.”

Saving Mr. Banks” is ostensibly about the sparring match of two creative titans: Disney is used to getting his way and has definite ideas about the movie he envisions, and Travers is stubborn and protective of the characters she has a personal attachment to.

The specific reason why Travers is so passionate about her book of “Mary Poppins” advancing onto the big screen won’t be discussed here. We know that Mr. Banks is a primary character in the Disney movie. But how and why Mr. Banks needs to be saved is an integral part of the abundant charm, and it’s best if this reveal evolves as the filmmaker intended.

As with the best based-on-fact films, “Saving Mr. Banks” does not purport to relate all the minutiae or give a full portrayal of each individual in that person’s life. That would reduce the impact of the story being told.

What makes the movie so amply appealing is the underlying theme: the importance of relating stories. There is immense power in storytelling, and reviewing incidents in our lives, through either writing or discussing them, can excise deeply personal and longstanding demons held deep within us.

Reviewers will quibble over how Disney is portrayed by the studio that still bears his name. But this is far from his film biography.

The screenplay by Kelly Marcel and Sue Smith is funny and whimsical, but mostly it’s heartbreaking and deeply affecting. Under the direction of John Lee Hancock, the actors give tremendous, award-worthy performances.

As the film begins, Travers (a superbly cast Emma Thompson, at the height of her abilities) travels from London to Hollywood where, after 20 years of back-and-forth phone calls, she agrees to meet Disney to review a screenplay draft. She needs the money that a sale of her book will generate, but that prompts the discussions rather than dictates them.

Travers meets the creative team — scriptwriter Don DaGradi (Bradley Whitford) and composers Robert B. and Richard M. Sherman (B.J. Novak and Jason Schwartman) — and immediately disputes the abbreviation of the script’s first word: “Int.,” for the stage direction of an interior film set.

The film intercuts flashbacks, a little on the long side, showing Travers’ life as a young girl and her loving relationship with her troubled father (Colin Farrell, who shines). Through this backstory of her own life, viewers see a misunderstood woman struggling with the memories of her difficult upbringing. Using the utmost care and sensitivity, Thompson takes us on an emotionally moving journey we had not anticipated.

Tom Hanks as Disney is compelling. He shows us a congenial and diplomatic man and how it was very natural for his associates to call him Uncle Walt.

What needs to be mentioned as well are the period-accurate details the designers so scrupulously wanted to bring to the screen. As a native Southern Californian with a longstanding interest in Disney’s company and its founder, it’s a joy to see so much of Disney’s office, studio exteriors and Disneyland as they appeared in the 1960s. From the precise placement and re-creation of the knickknacks behind Disney’s desk and the two sets of framed portraits of his daughters to the double helium Mickey balloons sold on Main Street — it’s enough to bring on goosebumps.

Remember that many Anaheim-area residents enjoy Disneyland as frequently as Utah skiers take to their favorite resort. And my work at the time involved visits to the studio, particularly to the extensive archives (where I was able to closely examine the snowglobe used in the filming of “Mary Poppins,” found by a janitor before being moved to a more protective home).

But whether you love all things Disney or consider “Mary Poppins” saccharine sweet, as Travers did, “Saving Mr. Banks” is effective and will be enjoyed — in the most delightful way.