A cocky American athlete named Lee Sheridan (Robert Taylor) receives a scholarship to attend Cardinal College, Oxford University in 1937. At first, Lee is reluctant to go to the college owing to his father Dan's (Lionel Barrymore) limited income, but he finally does attend. Once in England, Lee brags about his athletic triumphs to Paul Beaumont (Griffith Jones), Wavertree (Robert Coote), and Ramsey (Peter Croft) on the train to Oxford. Annoyed, they trick Lee into getting off the train at the wrong stop. Lee, however, does make his way to Oxford where the students attempt to trick him again, this time into thinking that he is getting a grand reception. Seeing through the deception, he follows the prankster impersonating the Dean and after chasing him is thrown off and ends up kicking the real Dean of Cardinal (Edmund Gwenn) before retreating. This begins a contentious relationship between them when Lee reports to apologize.
Lee considers leaving Oxford but stays on after being convinced by Scatters (Edward Rigby), his personal servant. Lee meets Elsa Craddock (Vivien Leigh), a married woman who "helps" the new campus students, and starts a relationship with Paul Beaumont's sister Molly (Maureen O'Sullivan). Lee makes the track team by outpacing other runners while wearing a cap and gown. Just when he begins to fit in, he is hazed for refusing to rest during a crucial relay race at a track meet and pushing his replacement Paul out of the way in his zeal to win. In a fit of anger, Lee goes to a pub, which students are forbidden to frequent, to confront Paul, finding him in a private booth with Elsa. He starts a fight with Paul but Wavertree warns them of the Bullers coming. Lee and Paul run and when they are almost caught by one of the Bullers, Lee punches him. Paul is called before the Dean, fined and warned for hitting the Buller. He is scorned for saying it was Lee who punched him and Lee is soon the favorite of Paul's old friends. Molly begins to see him again, but Lee still feels poor for what has happened between her and Paul.
Lee begins rowing for Oxford University Boat Club and in the bumps race for Cardinal's boat club, tries to make amends to Paul after winning a race, but Paul rejects the offer of friendship. Though his offer of friendship was rejected, Lee still helps Paul by hiding Elsa in his own room when Elsa is looking for Paul. The Dean catches the two of them together and expels Lee from Oxford. Lee's father comes for the races having not heard of Lee's expulsion from Oxford University. When Lee tells him that he had been having an affair with Elsa, Dan believes he is lying. Judging from Lee's letters about Molly he feels that Lee could not possibly have had an affair with Elsa due to the way he feels about Molly. Dan meets with Molly and the two devise a plan to get Lee back into college. Dan meets with Elsa at the bookstore and convinces her to talk to the Dean. After flirting with the Dean and telling him that Lee was only hiding her from Wavertree, Lee is allowed back into Oxford and Wavertree, who has spent the entire story trying to be expelled so he can come into an inheritance, receives to his disappointment only a minor punishment. Lee and Paul make amends and win the boat race.
A Yank at Oxford was MGM's first British production, with MGM head Louis B. Mayer taking a personal interest in casting. He visited the set several times. British playwright Roland Pertwee was one of several uncredited writers, and F. Scott Fitzgerald also spent three weeks working on the script, touching up rough points and adding bits of dialogue. Mayer and Balcon later got into a fight on set, within earshot of Vivien Leigh and Maureen O'Sullivan, that led to Balcon resigning as the producer.
To the surprise of other actors, Taylor was able to do all of the physical scenes himself, especially running and rowing. He had competed in track and field as a student at Doane College.
At first, Mayer was reluctant to cast the then little known Vivien Leigh in the role of Elsa Craddock, until persuaded by Michael Balcon, who stated that she was already living in Britain and it would cost much more to fly someone else out to England. During the filming of A Yank at Oxford, Leigh gained a reputation for being "difficult" to work with. According to her biographer Alexander Walker, Leigh felt judged by Maureen O'Sullivan, whom she had befriended years earlier at school, because O'Sullivan was happily married and Leigh was in the midst of an affair with Laurence Olivier and awaiting word of a divorce from her first husband, Leigh Holman. Therefore, the relationship was "strained." Also Leigh had developed a foot problem whereupon she asked to go to London to seek treatment. As Leigh was preparing to leave, the wardrobe department cut a hole in her shoes so that her toe would be at ease.
According to Leigh, she was forced to pay for her own shoes and demanded that MGM help her make some of the payments. On the other hand, MGM said that they bought all of Leigh's shoes and she didn't have to pay a penny on the film. Due to the dispute, her manager, Alexander Korda, sent Leigh a message stating that if her behavior did not improve, he would not renew her contract. Leigh's behavior did shape up and her contract was renewed.
Some film historians believe A Yank at Oxford was instrumental in getting Vivien Leigh noticed by David O. Selznick for Gone with the Wind. Regardless of her prior behavior, Leigh managed to make her way through the filming of A Yank at Oxford without much additional acrimony and made an impression on her costar, Robert Taylor. Taylor returned to Hollywood talking about the great English actress he had worked with and suggested to Selznick, who was still searching for his Scarlett O'Hara, that they ought to look at her.
A Yank at Oxford was reviewed by Frank S. Nugent in The New York Times as a "pleasant spoof." He noted, "... [it] turns out to be an uncommonly diverting show. It can't be the story, for we've read the one about the old college spirit before. ... It must be the accents, the caps and gown, the cycles and the remarkably credible chaps Metro hired to play dean and tutor, scout and students. When the camera turns upon them you can jolly well smell the fog, you know."
The film review in Variety concentrated on Taylor's appeal. "Robert Taylor brings back from Oxford an entertaining rah-rah film which is full of breathless quarter-mile dashes, heartbreaking boat race finishes and surefire sentiment—Metro's first British-made film under Hollywood supervision and with Hollywood principals and director."
A Yank at Oxford and its sequel, the 1942 A Yank at Eton, portrayed the British in a mainly positive light, and set the scene for other films that were popular in both the United States and the United Kingdom during the war years. The film was later parodied in the Laurel and Hardy film A Chump at Oxford (1940) and remade as Oxford Blues (1984) .
According to MGM records the film earned $1,291,000 in the US and Canada and $1,445,000 elsewhere resulting in a profit of $513,000.