He was born in Oxford, son of Wilford George Kendrew, reader in climatology in the University of Oxford, and Evelyn May Graham Sandburg, art Historian. After prep school at the Dragon School in Oxford, he was educated at Clifton College in Bristol, 1930–1936. He attended Trinity College, Cambridge in 1936, as a Major Scholar, graduating in chemistry in 1939. He spent the early months of World War II doing research on reaction kinetics, and then became a member of the Air Ministry Research Establishment, working on radar. In 1940 he became engaged in operational research at the Royal Air Force headquarters, holding the honorary rank of Wing Commander R.A.F. He was awarded his PhD after the war in 1949.