He was brought up in Oxford, as was educated at Eton College and Balliol College of Oxford University, reading mathematics. After a year working as a stockbroker, he started a Ph.D. in Princeton in differential geometry under Veblen in 1929. He worked also with Lefschetz. He became a fellow of Balliol in 1933. During the Second World War he worked on operations research for submarine warfare. He became a professor at Oxford in 1947.
His definition of CW complexes gave a setting for homotopy theory that became standard. He introduced the idea of simple homotopy theory, which was later much developed in connection with algebraic K-theory. The Whitehead product is an operation in homotopy theory. The Whitehead problem on abelian groups was solved (as an independence proof) by Saharon Shelah.
He was the nephew of Alfred North Whitehead.