Adrian was born at Hampstead, London, to Alfred Douglas Adrian, legal adviser to the Local Government Board, and Flora Lavinia Barton. He attended Westminster School and studied Natural Sciences at Trinity College, Cambridge, graduating in 1911 and in 1913, he was elected to a Fellowship of Trinity College on account of his research into the "all or none" law of nerves.
After completing a medical degree in 1915, he did clinical work at St Bartholomew's Hospital London during World War I, treating Soldiers with nerve damage and nervous disorders such as shell shock. Adrian returned to Cambridge as a lecturer and in 1925 began research on the human sensory organs by electrical methods.
Adrian married Hester Agnes Pinsent on 14 June 1923 and they had three offspring – a daughter and mixed twins:
A key result, published in 1928, stated that the excitation of the skin under constant stimulus is initially strong but gradually decreases over time, whereas the sensory impulses passing along the nerves from the point of contact are constant in strength, yet are reduced in frequency over time, and the sensation in the brain diminishes as a result.
Positions that he held during his career included Foulerton Professor 1929–1937; Professor of Physiology in the University of Cambridge 1937–1951; President of the Royal Society 1950–1955; Master of Trinity College, Cambridge, 1951–1965; President of the Royal Society of Medicine 1960–1962; Chancellor of the University of Cambridge 1967–1975; Chancellor of the University of Leicester 1957–1971. Adrian was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 1938. In 1946 he became foreign member of the Royal Netherlands Academy of Arts and Sciences. In 1942 he was awarded membership to the Order of Merit and in 1955 was created Baron Adrian, of Cambridge in the County of Cambridge.
