Composer Arthur Sullivan is torn between the world of "serious" and "light" music, as demonstrated by his oratorio The Prodigal Son and the operetta Trial By Jury, a collaboration with the writer William Schwenck Gilbert. His dilemma is thrown into sharp relief when his fiancée Grace walks out on him for wasting his musical gifts on triviality, a theme that will haunt the rest of his career.
Gilbert and Sullivan enter into partnership with the impresario D'Oyly Carte, though Sullivan insists that this is only a sideline to his work with the Royal College of Music. Their subsequent hits, The Sorcerer and HMS Pinafore, are played everywhere from barrel organs to brass bands, and pirated in America. To remedy this, the entire company goes on tour there, with a new work, The Pirates of Penzance, receiving a New York premiere. Afterwards, D'Oyly Carte announces that he will be opening a purpose-built theatre in the Strand.
The Savoy opens with Iolanthe. At the premiere, Sullivan revels in the atmosphere, while a clearly nervous Gilbert has to be placated by his wife. D'Oyly Carte opens the performance with a demonstration of the theatre's innovative electric lighting. While Sullivan conducts the performance, Gilbert goes for a long walk, getting back only just in time to take his curtain call.
Despite Iolanthe's success, Sullivan is unhappy. He rejects a proposal from Gilbert about a piece involving a magic lozenge, and claims that he wants to devote himself to serious music. In this he is supported by his friend, music critic Joseph Bennett, who writes a libretto for a serious cantata on Longfellow's The Golden Legend. But Gilbert has had another idea, inspired by the sight of a Japanese sword. Bennett calls on Sullivan expecting to hear the cantata being rehearsed, but hearing The Mikado instead. He informs Sullivan that Queen Victoria will attend the premiere of The Golden Legend if he ever gets round to writing it.
During rehearsals for The Mikado, D'Oyly Carte tells Gilbert that three numbers are missing. Gilbert goes round to see Sullivan, and finds him rehearsing The Golden Legend under Bennett's watchful eye. But when Bennett dozes off, Sullivan composes more of The Mikado. Both works are premiered, and Sullivan is knighted. The Queen asks him if he's ever going to write a grand opera.
Following the completion of Ruddigore, Sullivan asks Gilbert if he would write the libretto for his first serious opera. Gilbert expresses resentment that his words will play second fiddle to the music, and a huge argument ensues, during which Sullivan says that he no longer enjoys writing comic operas. The first night of Ruddigore is greeted with boos and negative reviews. Although financially successful, neither Gilbert nor Sullivan can be persuaded to write any more.
Helen D'Oyly Carte calls on Sullivan at Monte Carlo to tell him that her husband has decided to build another theatre, and would like a grand opera to open it with. Sullivan gladly accepts, and is then told that Gilbert has written another comic opera, The Gondoliers. Sullivan agrees to compose the music for that as well, and the result is another huge success.
Gilbert is stricken with gout, exacerbating an already foul temper. After examining the Savoy accounts, he goes to confront D'Oyly Carte at the new theatre to confront him over lavish expenses. During a subsequent stormy meeting with Sullivan, Gilbert announces that he will write no more operettas.
Sullivan's first serious opera, Ivanhoe, is premiered, and he presents a bound volume to the Queen. She proposes a private performance at Windsor, and startles Sullivan by requesting The Gondoliers. Sullivan gradually realises where his true gifts lie.
The D'Oyly Cartes toast a new century, hoping that it will see a revival of the Gilbert and Sullivan partnership. Gilbert pays a surprise visit to rehearsals for a revival of The Yeomen of the Guard and meets Sullivan, now confined to a wheelchair, for the first time in years. They make up, and propose taking a curtain call with D'Oyly Carte, all three of them in wheelchairs. But during the performance, Gilbert hears news of Sullivan's death. Many years later, he finally receives a knighthood of his own.