Massey published an autobiography in 2006, "Telling Some Tales", in which she revealed a difficult early life and discussed her failed marriage (1958–1962) to actor Jeremy Brett, discussing his struggle with bipolar disorder. Brett and Massey divorced on 22 November 1962 after she claimed he left her for a man. The couple had one son, writer and illustrator David Huggins (b. 1959). At an August 1988 dinner party held at the home of their mutual friend, Joy Whitby, she met Russian-born metallurgist Uri Andres, who had been based at Imperial College, London since 1975. The couple were married from November 1988 until her death in 2011.