The mention of the headless man in A Very British Scandal is a key element of both the show and the real-life case it was based on. A Polaroid image of the headless man (called that because his head was not visible) was presented at the Duke and Duchess' divorce hearing. Although faces are not visible, a woman wearing a pearl necklace similar to the one that Margaret often wore was seen performing oral sex on an unidentified man.
This is a key element of the show as the entire program focuses on Margaret and Ian's relationship dissolving very publicly. Per The Scotsman, Ian accused Margaret of cheating on him with 88 other men. However, it was revealed later that many of the men were homosexual and that she was keeping their sexuality a secret because it was a punishable offense in the UK at the time.
In A Very British Scandal, Margaret confesses that she was the one in the photos, but does not reveal the man's identity. In reality, Margaret's association with the photos remained with her until her death on July 25, 1993, and like on the show, she never officially revealed who the man in the photo was.