Cockcroft, who was born at Todmorden in northern England, entered Manchester University in 1914 to study mathematics, but left the following year to join the army. After World War I he was apprenticed to the engineering firm Metropolitan Vickers, which sent him to read electrical engineering at the Manchester College of Technology. He later went to Cambridge University, graduated in mathematics, and joined Ernest Rutherford's team at the Cavendish Laboratory.

Cockcroft soon became interested in designing a device for accelerating protons and, with E. T. S. Walton, constructed a voltage multiplier. Using this Cockcroft and Walton bombarded nuclei of lithium with protons and, in 1932, brought about the first nuclear transformation by artificial means: ⁷ ₃Li + ¹ ₁H → ⁴ ₂He + ⁴ ₂He + 17.2 MeV

For this work Cockcroft and Walton received the 1951 Nobel Prize for physics. During World War II Cockcroft played a leading part in the development of radar. In 1940 he visited America as a member of the Tizard mission to negotiate exchanges of military, scientific, and technological information. In 1944 he became director of the Anglo-Canadian Atomic Energy Commission. He returned to Britain in 1946 to direct the new Atomic Energy Research Establishment at Harwell and remained there until 1959, when he was appointed master of Churchill College, Cambridge, a new college devoted especially to science and technology. Cockcroft received a knighthood in 1948.