Goodbye Gemini (aka Twinsanity) is a 1970 British thriller starring Judy Geeson, Michael Redgrave, and Martin Potter. Directed by Alan Gibson, it was based on the novel Ask Agamemnon by Jenni Hall. The film concerns a pair of unusually close fraternal twins, Jacki and Julian, discovering Swinging London while home on Spring Break. Their experiences complicate the pair's relationship, which is already strained due to Julian's incestuous fascination with his sister, which he sees as a natural manifestation of what he believes to be the pair's hive-minded nature.
The film was produced at a time when conservative groups were beginning to react to the perceived social excesses of 1960s British culture. Coincidentally, it was released concurrently with Freddie Francis' Mumsy, Nanny, Sonny and Girly, another horror film which also dealt with an unusual familial relationship and contained a scene implying consensual brother-sister incest. Gemini and Girly were targeted by the conservative press as endemic of everything wrong with contemporary British culture, resulting in protests and theaters refusing to show the films. The two pictures were ultimately banned in the UK, with Gemini being listed as a video nasty.
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.