Alexander was born Frances Elizabeth Somerville Caldwell on 13 December 1908 in Merton, Surrey.[2] She spent some of her early life in India, where her father, Dr. K. S. Caldwell, was a professor at Patna College. (He was later principal of Patna Science College after its founding in 1928).[3] In 1918, Alexander returned to the United Kingdom and began secondary school.