Goodbye Gemini
Unnaturally close twin siblings Jacki (Judy Geeson) and Julian (Martin Potter) become enmeshed in the swinging London scene, where they attract the attention of the heavily endebted gambler Clive (Alexis Kanner). Seeing a way out of his debts, Clive sets Julian up for a blackmail scheme, setting in motion a nightmarish sequence of events.
Jacki (Geeson) and Julian (Potter) Dewar, a pair of fraternal twins, arrive via bus in London on Spring break from university, while their father is in Mexico on business. The pair launch themselves into London's underground party scene, clubbing at strip bars, accompanied by Jacki's teddy bear, Agamemnon, whom the twins address—and regard—as a father figure. At one club the pair encounter Clive, a small-time pimp who survives by ingratiating himself with the wealthy and well-connected. Clive quickly endears himself to Jacki, while Clive's sometimes girlfriend Denise attempts to seduce Jules. Julian turns her down, intent on beginning an incestuous relationship with Jacki. Julian regards he and his sister as two halves of a hive mind, and sees incest as a natural expression of their closeness.
It becomes apparent that Clive is using Jacki and Jules' house to hide from a gangster to whom he owes a large gambling debt. One night after Jacki turns down Jules' advances, Clive plies him with whiskey and marijuana and takes him to a brothel where Clive keeps his "Circus"—a group of transvestite prostitutes who work for him. On Clive's orders, two of the prostitutes anally rape Julian while Clive takes photos.
Clive attempts to blackmail Julian with the photos in order to pay off his gambling debt. Meanwhile, Denise reveals the plan to Jacki, telling her that Clive has similarly raped and blackmailed other men in the past, going to far as to sell some of them into sexual slavery when they were unable to pay him. That night, Jacki comforts Julian, telling him that she knows what happened and that their relationship has not changed.
The next night, the twins bet a drunken Clive that he can't tell the two of them apart. Clive agrees, and the twins quickly dress the room in a ritualistic manner, erecting an "altar" for Agamemnon and dressing themselves in bed sheets altered to look like ceremonial robes. When Clive hesitates in identifying them properly, the twins stab him to death with Jacki's antique Tantōs. In the process of Clive's murder, Agamemnon is cut in half; upon seeing the bear, Jacki suffers a nervous breakdown and she flees, leaving Julian behind.
Jacki is discovered semi-catatonic on a dock by member of parliament James Harrington-Smith, who recognizes her from a party. Jackie, now suffering amnesia, slowly recovers at James' flat as she attempts to piece together what happened the night of Clive's death. Her discovery of Clive's body upon returning home inadvertently causes a citywide manhunt for both siblings; James lies to the police about Jacki's whereabouts the night of the murder, allowing blame to be shifted solely onto Julian.
Deducing that Julian has gone to hide in the same hotel where Clive kept his Circus, Jacki tells James that she'll convince him to turn himself in and to call the police if she hasn't returned after an hour. Jacki confronts Julian, whose mental state is rapidly deteriorating. Julian insists that all of their problems are a result of the pair not engaging in an incestuous relationship, which Julian believes would reinforce their "specialness" to the world. Meanwhile, James, fearful of the potential political scandal that could result from his connection to the twins, decides not to call the police.
Jacki attempts to convince Julian that she'll help him escape London, intending to return to James with information on Julian's whereabouts. An increasingly paranoid and delusional Julian attacks Jacki and crushes her windpipe, killing her. In a moment of lucidity, a distraught Jules apologizes to the dead Jacki before blowing out the room's pilot light and gassing himself to death.