In 1949, Davis married the soprano April Cantelo. They had two children, Suzanne and Christopher. Their marriage ended in 1964, and in that same year, Davis married the young Iranian woman who had been the family "au pair", Ashraf “Shamsi” Naini. To satisfy both the Iranian and British authorities, the couple were married three times, once in Iran and twice in the UK, in the Iranian Embassy as well as in a regular UK civil ceremony. They have five children.