In 1937, a cocky American athlete, Lee Sheridan [Robert Taylor], wins a scholarship to Cardinal College, Oxford. Initially reluctant because his father, Dan [Lionel Barrymore], has limited income, he still journeys across the Atlantic to prove himself. On the train to Oxford, he boasts about his athletic triumphs to Paul Beaumont [Griffith Jones], Wavertree [Robert Coote], and Ramsey [Peter Croft], and the trio decide to teach him a lesson by getting him off at the wrong stop. Lee eventually makes it to Oxford, where the students stage another ruse—this time a grand reception—that he sees through. He chases after the impersonator pretending to be the Dean and, in a brief confrontation, ends up shoving the real Dean of Cardinal [Edmund Gwenn], before retreating. This misstep kicks off a tense, uneasy relationship with the Dean and the college authorities.
Lee contemplates leaving, but is encouraged to stay by Scatters [Edward Rigby], his scout. He soon meets Elsa Craddock [Vivien Leigh], a married woman who “helps” the new students, and begins a complex relationship with Molly Beaumont [Maureen O'Sullivan], Paul’s sister. Determined to prove himself, Lee earns a place on the track team, even outpacing rivals while wearing a tweed suit, cap, and gown. Just as he starts to fit in, he refuses to rest during a crucial track meet against Cambridge and pushes Paul’s stand-in out of the way in his zeal to win, silencing the astonished crowd.
That night, the new cardinal hazing—funeral march music and debagging—unfolds, and Scatters explains the tradition: the win isn’t celebrated as a true victory. Lee later confronts Paul in a pub (out of bounds to students) and finds him with Elsa. A fight erupts, but Wavertree warns them that the Oxford police, the “Bullers,” are coming. Lee and Paul bolt, and Lee ends up punching the Buller himself. Paul is summoned before the Dean, fined for hitting the Buller and for associating with Elsa, and, when he reveals that Lee was the instigator, Lee is content to let Paul take the blame. Despite this, Lee soon becomes part of Paul’s circle again, and months pass.
Molly begins dating Lee, while Paul quietly sees Elsa again. Lee joins the Oxford University Boat Club and is chosen as Cardinal’s stroke for the bumps race. After the race, he tries to mend fences with Paul, but Paul rebuffs him. Elsa’s wild flirting resumes, and she begins a seduction with another student, only for her husband to intervene. Elsa then seeks Paul, with Craddock pursuing; Lee hides Elsa in his room, and when the Dean learns of the affair, he expels Lee from Oxford. A crowd escorts Lee to the train station, where Dan has just arrived, unaware of Lee’s expulsion or the letters that claimed otherwise about his relationship with Elsa. Dan arranges a reunion with Molly, and they plot to get Lee back into the college. Dan convinces Elsa to speak with the Dean, and after flirting with him and claiming Lee hid her from Wavertree, Lee is allowed back. Wavertree realizes his own scheme to be expelled and faces only a minor punishment. Paul renews his friendship with Lee, and Oxford wins The Boat Race, though Paul faints from the exertion. The Craddocks move to Aldershot, near the Officers Club, closing the chapter on this high-spirited, turbulent chapter of Oxford life.