In 1968, he met Vicki Hodge, a baronet's daughter turned model and actress, who introduced him to British aristocracy. However, he had been previously invited to the Caribbean island resort of Mustique, where Bindon claimed to have had sex with Princess Margaret. The biographer of the Princess, Noel Botham, was also of the opinion that Bindon had an affair with her. During this time Bindon gained the nickname "Big John", due to the reported size of his penis. He went back to Mustique for a second time in 1969 and took girlfriend Hodge with him. The princess later publicly denied meeting Bindon (despite pictures of them next to one another) and was reportedly unimpressed to hear stories of their sexual encounters in the press. Bindon's name was also linked with a succession of models, including Christine Keeler, the former Playboy "Bunny Girl" Serena Williams, and also Angela Barnett, then girlfriend and future wife of pop star David Bowie.
Bindon was awarded the Queen's Award for Bravery, a police bravery medal, for diving off Putney Bridge into the River Thames to rescue a drowning man, in 1968, although some said he had pushed the man in and only rescued him when a policeman appeared.