The son of a lawyer, Hume-Rothery was born at Worcester Park in Surrey. He originally intended to pursue a military career and consequently entered the Royal Military Academy, Woolwich, on leaving school. An attack of meningitis which left him totally deaf forced him to leave the army and he turned instead to chemistry. Although refused entry to his father's college, Trinity College, Cambridge, because of his deafness, he was more graciously received by Magdalen College, Oxford. After obtaining his PhD from the Royal School of Mines in 1925, Hume-Rothery returned to Oxford where he remained for the rest of his life, being appointed in 1958 to the university's first chair of metallurgy.

With 178 published papers to his credit Hume-Rothery illuminated many areas of metallurgy. His best-known work was concerned with alloys that are solid solutions, in which atoms of the constituent metals share a common lattice. The Hume-Rothery rules give the conditions that have to be satisfied for metallic solid solutions to form. The first concerns the atomic size factor and claims that if the atomic diameter of the solvent differs in size from that of the solute by more than 14%, the chances of solubility are small. Secondly, the more electronegative is one component and the more electropositive the other, the more they are likely to form compounds rather than solutions. And, finally, a metal of lower valency is more likely to dissolve one of higher valency than vice versa. Much of his work in this field was published in his book The Structure of Metals and Alloys (1936).