On 7 June 1944, Elliot married Donald James Graham Gowing at the Wimbledon Registry Office. He was a vocalist who had also attended Christ's Hospital before winning a choral scholarship to Kings College, Cambridge, in 1939. He had joined the Royal Naval Volunteer Reserve in 1941, and was serving at Combined Operations Headquarters. They married shortly before he was shipped overseas. He was taught Japanese in the United States and went on serve in the Pacific as a translator. The marriage bar was suspended for the duration and Gowing was allowed to remain in the Civil Service. They had two children, both sons: Nicholas Keith (Nik), a journalist who was born in 1951 and named after Hancock, and James, born in 1954. Her husband, frustrated by his lack of professional success compared to hers, became an alcoholic, and died from a massive stroke in 1969.