For those who feel they have grown out of Walt Disney - and for those who happily have not - Saving Mr Banks is a delightful slice of grown-up whimsy, befitting the man himself, about the making of one of his most famous films.

It is based on the real-life difficulties Disney experienced in persuading the British writer PL Travers to sell the film rights to Mary Poppins. Annually for 20 years the filmmaker approached the writer, and each time she refused. In 1961 he finally cracked her resolve.

The film's principal focus is on Travers (Emma Thompson). Flitting back and forth between the 1960s and her childhood at the turn of the century in Australia, it reveals the formative family experiences that inspired her Poppins stories, then fuelled her reluctance to hand them over to the creator of Mickey Mouse.

In 1906, in Queensland, young "Ginty" and her family move from a comfortable urban home to a rural backwater, as doting dad Travers Goff (Colin Farrell) struggles to keep himself employed. Flamboyant but alcoholic, Goff prefers to indulge in flights of fancy with his daughter than go to work at the bank. The inference is that this tragic man is the font of his daughter's creativity, as well as the template for the Mr Banks of the stories; it's not Mary that Travers can't let go, but her father.

In 1961, the woman who refuses to be addressed by her first name steps on board a plane for Los Angeles. By the time she has verbally mauled her agent, been rude to a stewardess and inquired, "Will the child be a nuisance?" it is clear she is not a particularly pleasant woman. Doesn't it smell of jasmine, suggests her driver (Paul Giamatti) enthusiastically when she lands in LA. "Chlorine and sweat," she retorts.

Disney (Tom Hanks) has arranged for his creative team to present their adaptation to the author and deal with her objections, so that she will sell the rights; despite needing the money, Travers's plan is to find fault until they give up hope. A civilised yet cunning battle of wills ensues.

Structurally, there are far too many flashback scenes, labouring their point, when the fun to be had is in the sparring between Disney and Travers - the Hollywood mogul with a popular touch and the children's author who does not like anyone, let alone kids - with a dash of culture clash for good measure.

"Where is the gravitas?" exhorts Travers, as she torments the songwriting Sherman Brothers (cutely played by Jason Schwartzman and BJ Novak) and flustered screenwriter Don DaGradi (The West Wing's Bradley Whitford). Disney having agreed not to make an animated film (somewhat disingenuously), she now fixes on the music. "Mary Poppins does not sing." The Shermans shuffle Super­califragilisticexpialidocious out of sight.

Thompson delivers the writer's haughty authority to perfection. But the glory of the film is Hanks's performance as Disney, which captures the shrewdness of a man used to getting what he wants, with genuine exasperation as to why Travers is so resistant. There are moments, too, where he transmits the frisson of inspiration that was apparently Disney's forte. "This is what we storytellers do," he tells Travers, as he begins to realise the sadness behind her barricade, "we instil hope, again and again and again."

Beneath the sugar coating is an interesting reflection on the difficulty artists have in letting go of their work, for whatever reason. Make sure to stay for the credits, and the tape recordings of the real Travers holding on for dear life.