The film commences on October 12, 1978, as several police officers forcibly drag Sid Vicious out of the Hotel Chelsea in the wake of his girlfriend, Nancy Spungen, being found dead. Once at the police station, Sid is confronted and asked to recount the events leading to this tragedy, but he struggles to articulate his thoughts, leaving the officers visibly frustrated by his turmoil.
Backtracking to 1977, we witness the beginnings of Sid's involvement with Nancy, a heroin-dependent groupie who makes her way to London with aspirations of sleeping with the Sex Pistols. Although Sid initially rebuffs her advances, he soon finds himself drawn to her after witnessing the rejection she endures from other punk icons and after she introduces him to heroin—a critical turning point in their lives. Their romance deepens, but it is steeped in self-destructive behaviors fueled by drugs, which ultimately strains Sid's relationships with his bandmates. The band breaks up on January 17, 1978, amidst a disastrous American tour wherein Sid’s addiction spirals out of control, rendering him often intoxicated and dangerously volatile. Despite the repeated warnings from friends about Nancy's detrimental influence, Sid stubbornly chooses to disregard their advice.
As the narrative unfolds, we find Sid in New York, attempting to carve out a solo career with Nancy managing him. However, he is quickly regarded as a relic of the past. As both slip deeper into heroin addiction, Nancy begins to wrestle with her own demons, descending into severe depression. Sid's feelings for Nancy begin to wane, leading him to seek an escape from the suicide pact they had once entered into together. Their relationship reaches a tragic climax during a night of heated argument, sparked by Sid's declaration to quit heroin and return to England for a fresh start. Conflicted and desperate, Nancy begs him to end her life; in a drug-fueled rage, they engage in a physical confrontation that results in Sid stabbing her, leaving the intent ambiguous.
After their fateful encounter, Sid and Nancy fall asleep, and later Nancy, in a disoriented state, stumbles into the bathroom where she tragically collapses and dies. Sid, momentarily bailed out by his own mother—who also struggles with addiction—finds some fleeting joy in dancing with a group of children after grabbing a pizza. In a moment of surrealism, a taxi picks him up, and he believes he sees Nancy alive in the backseat. Their tender embrace unfolds as the cab drives off, symbolizing the tragic intertwining of their lives. A poignant postscript reveals that Sid eventually succumbed to an intentional heroin overdose, sharing a grave with Nancy, marked by the inscription: "R.I.P. Nancy and Sid."
