Richard Sherman and his late brother Robert wrote some of the most beloved songs in movie musicals, including “Trust in Me” from “The Jungle Book,”  “Chitty Chitty Bang Bang” from the musical of the same name, the theme to “Winnie The Pooh,” and “Bedknobs & Broomsticks’” “The Age of Not Believing.”  But it is for their work on “Mary Poppins” that they are most remembered through such songs as the Oscar-winning “Chim Chim Cher-ee,” “Supercalifragilisticexpialidocious,” “A Spoonful of Sugar” and “Feed The Birds.”

“Saving Mr. Banks,” which opens wide Friday (20), tells the true story of how Walt Disney spent 20 years trying to woo “Mary Poppins” book author P.L. Travers into signing over the rights to create a movie about the beloved nanny. More specifically, the film deals with a two-week period in 1961 during which The Sherman Brothers (played by Jason Schwartzman and B.J. Novak), writer Don DeGradi, and British author Travers struggled to come up with a story line for the film that would meet her approval.

“Those two weeks I would hate to go through again,” Sherman, 85, says. Even though he loved “Mary Poppins,”  working with Travers was even worse than it appears in “Saving Mr. Banks,” he says. “Mrs. Travers was very, very difficult.”

He adds that neither he nor his brother knew anything of her backstory that the movie lays out: that she was raised in Australia as Helen Gough and that she spent much of her young life dealing with her charming, yet alcoholic, father.

In addition to handling the taciturn, stubborn Travers, the Shermans, Disney, and DeGradi had to deal with the fact that her book didn’t have much of a plot. “When we first read the books, we thought ‘There’s no story here. We have to tell the story,” he says. “There’s a reason Mary Poppins comes. It’s because it’s an unsettled household. The father’s paying no attention and the mother is off with the suffragette movement. This is stuff we trumped up.”

Disney loved the plot twists that the Shermans help devise, as well as their songs for “Mary Poppins,” but he was often spare with his compliments to their faces. “He never said anything was great,” Sherman says. “Behind our back, he’d say he loved our songs, but [to us], he’d say, ‘That’ll work.’ That was his praise. That’s what he said to everybody.”

Sherman, who worked as a consultant on “Saving Mr. Banks,”  told screenwriter Kelly Marcel such nuances, which found their way into the script and then into Tom Hanks’ portrayal of Disney. Of the fact that his brother, Travers, DaGradi, and Disney have all passed, leaving him the only one with first-hand knowledge of the story, Sherman ruefully says, “I’m the last one standing.”

For Sherman and his brother, Disney “was like a second father. We both loved him.” In fact, he quickly rises to Disney’s defense when reminded that Disney’s legacy has been tarnished by accusations of racism and anti-semitism. “Let me tell you something, a lot of people talk about Walt in negative ways. There was nothing negative about Walt Disney,” he says. “He was dedicated to doing great things. He reached for the stars all the time. He was a wonderful, wonderful boss.”

“Mary Poppins” blew the Sherman Brothers’ careers wide open. They became staff writers as Disney and worked on dozens of projects for both the Mouse and other studios over the decades. Sherman continues to write, often feeling his brother’s spirit with him. But he often thinks back to “Mary Poppins.” “It meant so much to us,” he says. “We knew this would be the doorway to our success as songwriters because we had been writing songs and had a couple of hits, but nothing huge. This was a huge thing for us.”