It’s nearly impossible not to like this literate period drama that relocates the “Rocky” formula from the boxing ring to the royal palaces of pre-World War II Great Britain—especially when instead of Sylvester Stallone you get Colin Firth as the Duke of York, with Geoffrey Rush standing in for Burgess Meredith as his trusty trainer.

The Duke’s problem, of course, wasn’t that he didn’t have a good right hook. It’s that he suffered from a pronounced stammer that made public speaking torturous both for him and for his listeners, a circumstance “The King’s Speech” cunningly dramatizes in an opening sequence set at the British Empire Exhibition in 1925, when a large crowd—as well as his own wife (Helena Bonham Carter)—react with pained sympathy as Prince Albert struggles to open the ceremony, his cheeks puffing out hopelessly and only guttural sounds emerging. It’s after this that the Duchess, giving up on the efforts of specialists to cure her husband through the old marbles-in-the-mouth method that worked for Demosthenes, seeks out a very different sort of therapist, a failed Australian actor named Lionel Logue (Geoffrey Rush). (One of the most amusing scenes in the picture shows Bonham Carter being driven to Logue’s unprepossessing office through the London fog, with an attendant literally walking ahead of the car to guide it along.)

It’s the relationship that develops between the Duke and Logue that’s the core of “The King’s Speech.” The exuberant Logue refuses to meet with clients anywhere but in his drab office, and his methods are idiosyncratic. In particular he treats the Duke as an equal, calling him “Bertie” much to the royal’s chagrin, and encourages him to sing and curse to get words out. Most importantly, though, he gets the prince to open up about the domestic torments that he believed (as a psychologist in all but name) to be at the root of the problem. Albert eventually reveals his father George V (Michael Gambon) bullied him, that he was forced to use his right hand though a natural leftie, that his nanny mistreated him, and that he had to wear painful leg braces much of his childhood. As the revelations mount and the social boundaries between them break down, the Duke and Logue become unlikely friends, though there are bumps along the way.

Albert’s impediment escalates from the personal to the political, however, when his father dies and his wayward brother King Edward VIII (Guy Pearce) decides to resign the crown to marry Wallis Simpson (Eve Best), the American divorcee with whom he’s utterly besotted. That will thrust Albert into the limelight as monarch just as war looms with Nazi Germany and he will have to give a radio address to rally the nation—and the entire Commonwealth—to the cause. (The picture’s title, of course, refers to both the Duke’s mode of speaking and the big speech he’ll have to give.)

This is a tale that brings together two very different elements, each of which will have appeal among a certain audience (older, better educated, less prone to judge a movie by the number of explosions and fistfights). One is the allure of British upper-class drama, which attracts not only lovers of period pieces but, in thus case, those fascinated with the royals (just as “The Queen” did). The other is the underdog theme, which celebrates the ultimate triumph of those who start out from a place of disadvantage (something true not only of the Duke, with his impediment, but of Logue, who’s an outsider by nationality, of course, but also because of his lack of proper medical “credentials”—something that becomes the inevitable third-act obstacle in David Seidler’s script). Thus we get the uplifting finale when George VI delivers his radio address as Logue literally conducts him, beaming, all to the strains of Beethoven’s Seventh Symphony. Naturally everyone—including the technicians—applauds when he finishes, and many viewers may feel like cheering, too. “The King’s Speech” goes “Rocky” one better by giving you two people to root for.

Needless to say, a project like this is also attractive to the upper echelons of acting royalty. Firth towers above his co-stars with a stunning performance that captures the Duke’s suffering while making the man utterly sympathetic (showing his affection for his daughters as well as his exasperation with his brother). But Rush, one of no fewer than eleven co-producers, is great as well, exulting in the showy role of Logue, the sort of voluble but sensitive eccentric one can’t help but like. These two dominate the proceedings, but a virtual gallery of eminent thespians stroll across the stage in lesser roles, most notably Bonham Carter (who’s delightfully matter-of-fact), but also Gambon (imposing, but touching after he’s fallen ill) and Pearce (appropriately reckless). Then there are Timothy Spall as Churchill, Anthony Andrews as Stanley Baldwin, Derek Jacobi as the Archbishop of Canterbury and the still-radiant Claire Bloom as Albert’s mother Mary. If there’s a weak link in the cast it’s Eve Best, who’s instructed to play Wallis Simpson as a posturing prima donna.

That’s about the only flaw in Tom Hooper’s direction, which is otherwise assured and straightforward. And his behind-the-camera team works wonders with the period recreation, from production designer Eve Stewart and art director Leon McCarthy to set decorator Judy Farr and costume designer Jenny Beavan; happily cinematographer Danny Cohen captures every detail. And though the score is attributed to Alexandre Desplat, what you’re likely to recall are the classical pieces used—not just Beethoven’s Seventh but some well-chosen Mozart (the “Figaro” overture and the clarinet concerto).

Like all docu-dramas, “The King’s Speech” selects, abbreviates, and manipulates. But in this case, you won’t mind. This plush, evocative slice of British royal history is also an irresistible portrait of an unlikely friendship and a rousing tale of triumph over adversity.