Born in Budapest, Hungary, he was the son of Elisabeth (née Diamounstein) and Gyula Medak, a textile manufacturer. His family was Jewish. In 1956, he fled his native country for England due to the Hungarian Revolution. There he embarked on a career in the film industry, starting as a trainee and gradually rising to the position of film director.
His first wife, with whom he had two children, died in London in the 1970s. He had two further children with his second wife, the English actress Carolyn Seymour, from whom he was later divorced. Medak was then married to opera singer Julia Migenes from 1988 to 2003.