Eckersley was born in London. He was educated at Bedales School, University College, London, where he gained a degree in engineering, and Trinity College, Cambridge, where he gained a second degree in mathematics. In 1919 he joined the Marconi Company as a theoretical research engineer and stayed there for the remainder of his career. He devoted most of his career to research into radio waves reflected downwards from the Heaviside layer and how they interfered with direction finding equipment.
Eckersley's mother Rachel was the fifth child of Victorian biologist Thomas Henry Huxley renowned for his advocacy of Charles Darwin's theory of evolution. Eckersley's younger brother was the BBC engineer Peter Eckersley.
In 1920, Eckersley married author Barry Pain's, daughter Eva Amelia.
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