Hewish was born at Fowey in Cornwall, and studied at Cambridge University. He obtained his BA in 1948 and his PhD in 1952 after wartime work with the Royal Aircraft Establishment, Farnborough. He lectured in physics at Cambridge until in 1969 he was made reader and in 1971 professor of radio astronomy, becoming professor emeritus in 1989. In 1974 he was awarded the Nobel Prize for physics jointly with Martin Ryle.

One of Hewish's research projects was the study of radio scintillation using the 4.5-acre telescope, which consisted of a regular array of 2048 dipoles operating at a wavelength of 3.7 meters. Radio scintillation is a phenomenon, similar to the twinkling of visible stars, arising from random deflections of radio waves by ionized gas. The three types of scintillation are caused by ionized gas in the interstellar medium, in the interplanetary medium, and in the Earth's atmosphere. All three types were discovered at Cambridge and Hewish was involved in their investigation. In 1967 a research student, Jocelyn Bell (later Bell Burnell), noticed a rapidly fluctuating but unusually regular radio signal that turned out to have a periodicity of 1.337,301,13 seconds. She had discovered the first pulsar.

To determine the nature of the signal, Hewish's first job was to eliminate such man-made sources as satellites, radar echoes, and the like. Measurements indicated that it must be well beyond the solar system. It seemed possible that it had been transmitted by an alien intelligence and the LGM (Little Green Men) hypothesis, as it became known, was seriously considered at Cambridge, but with the rapid discovery of three more pulsars it was soon dropped.

Hewish did however manage to establish some of the main properties of the pulsar from a careful analysis of its radio signal. Apart from its striking regularity (it was later shown to be slowing down very slightly) it was extremely small, no more than a few thousand kilometers, and was situated in our Galaxy.

By the end of February 1968 Hewish was ready to publish. His account received wide publicity in the popular press and stimulated much thought among astronomers as to the possible mechanism. The proposal made by Thomas Gold and others that pulsars were rapidly rotating neutron stars has since won acceptance.