Negro engineer Mark Thackeray (Sidney Poitier) arrives at the North Quay Secondary School in London's tough East End where he's recently been employed in a teaching position after having been turned down for engineering positions throughout England, and is taking this job to make ends meet while continuing to look for a job in his field.
The North Quay staff offer varying opinions about students at the school. The cynical Mr. Weston (Geoffrey Bayldon) is openly contemptuous of them. New hire Gillian Blanchard (Suzy Kendall) is admittedly afraid of them. Deputy Head Evans (Faith Brook) and Clinty Clintridge (Patricia Routledge) warn that while they're mostly good kids, they come from rough homes and excel at riding roughshod over teachers. Headmaster Florian (Edward Burnham) explains that they've been principally rejected from other schools. The audience is informed that their antics drove their last teacher to resign.
The students more than live up to their reputation. Led by Bert Denham (Christian Roberts) and Pamela Dare (Judy Geeson), they're an unruly mob who view the classroom as their domain. A battle of wills ensues. As the students' antics progress from mere disruptive behavior to distasteful pranks, Thackeray retains his calm manner and resists being baited. A turning point comes, however, when one morning he discovers something (presumably a sanitary pad) burning in the classroom grate. He angrily orders the boys out of the classroom and excoriates the girls for their disgusting, "sluttish" behavior. Dismayed by his lack of self-restraint, he retreats to the staff room, upset that he let himself be manipulated by "kids."
Returning to the classroom, Thackeray outlines a new approach to teaching his students and sets strict ground rules. The students will be leaving school and entering the adult world soon. His new strategy is to treat them as adults and allow them to discuss issues of their own choosing. He emphasizes this by throwing out all their textbooks. As part of being adults, he insists the students will use proper forms of address (both toward him and amongst themselves) and take pride in their appearance and deportment.
While Denham continues to bait Thackeray, the rest of the class is won over. Although Thackeray's humble background is quite like their own, he's made a success of himself by cultivating his language and dress. He insists they can do the same if they wish.
Unexposed to the rich history and culture of their own city, the students are especially excited when he suggests they go on a class outing to the British History Museum. The Headmaster is reluctant but issues approval, and Thackeray arrives on the morning of the trip to find a classroom of well-dressed, well-scrubbed students. The outing is depicted in a photo montage of the students enjoying themselves among the sculptures and art.
There is a darker turn when the gym teacher, Mr. Bell (Dervis Ward), insists that Carl 'Fats' Buckley (Roger Shepherd) participate in vaulting, despite his classmates' objections. The vault collapses and breaks under Buckley's weight. Although Buckley is not seriously hurt, the boys are angry at the coach for forcing him to attempt the jump. Picking up the vault's broken leg, Potter (Chris Chittell) threatens Bell with it. Thackeray is called to defuse the situation.
In class, Thackeray demands that Potter apologize to Bell for the incident even if he believes Bell was wrong. At this point Thackeray has lost the support of much of the class, especially the boys. They refuse to invite him to the class dance, and when Seales' (Anthony Villaroel) [the only black student in the class] mother dies, the class takes up a collection for a wreath but refuses to accept Thackeray's donation. At this point, the Headmaster advises Thackeray that as 'the adult approach' has failed, future class outings are cancelled, and Thackeray will take over the boys' gym classes.
Pamela's mother comes to speak with Thackeray, concerned that Pamela is staying out late and might be getting into trouble. Thackeray agrees to speak with Pamela, who insists her mother does not care about her and that the presence of male callers at her mother's house excuses her behavior. Thackeray maintains that Pamela still owes her mother respect, and disillusioned, she angrily accuses him of being 'just one of them'. She also refuses to take the flowers to Seales' mother's funeral. Thackeray's split with the class is complete.
Thackeray's search for an engineering position has continued throughout the movie, and at this low point in his relationship with his students, he is ecstatic to receive a job offer.
In gym, Denham insists they have a boxing lesson, beginning with him and Thackeray. Thackeray reluctantly agrees. Despite getting in some early blows, Denham is disabled when Thackeray throws a massive abdominal punch that knocks the wind out of him. Thackeray draws back his fist to hit Denham again but gains control of his emotions and declares the fight over.
Afterward, Denham waits to speak with Thackeray in the stairwell. Although Denham admits he was trying deliberately to hurt Thackeray in order to convince him to resign from teaching, Denham is surprised that Thackeray did not capitalize on his advantage. For his part, Thackeray admits that he lost his temper but that he understands the apparent unfairness of some of his decisions. Thackeray then offers to recommend Denham for a position as a boxing instructor to the younger students next term.
Surprised that he would be regarded as a potential teacher, Denham nevertheless promises to consider it. Denham is clearly impressed, and expresses his admiration for Thackeray to his fellow students. By winning Denham over, Thackeray wins back the respect of the rest of the class, and he is invited to the class dance. When he shows up at the Seales funeral, he is greeted by the entire class, who has come to pay their respects.
At the dance, all has clearly worked out well. Weston admits that Thackeray is really quite a gifted teacher and should reconsider leaving. The Deputy Head concurs, suggesting that he should go to another school, if nothing else. Barbara Pegg (Lulu) announces a "ladies' choice" dance and Pamela singles out Thackeray as her partner. Denham announces that the class has 'something special' for Thackeray and Miss Wong presents him with a pewter mug while Lulu sings the movie theme. Thackeray is too moved for words and retires to his classroom.
Breaking Thackeray's solitude in the dark silence of his classroom, a young boy and girl burst in, not aware of the teacher's presence. Upon seeing him they begin mocking his gift and joking that they will be in his class next year. When they leave, Thackeray rises, ponders his situation, then retrieves the job offer from his pocket and rips it to pieces.