He attended King's College, Taunton. His undergraduate degree at Gonville and Caius College, Cambridge, was interrupted by war Service at the Royal Aircraft Establishment, and at the Telecommunications Research Establishment where he worked with Martin Ryle. Returning to Cambridge in 1946, Hewish completed his degree and immediately joined Ryle's research team at the Cavendish Laboratory, obtaining his PhD in 1952. Hewish made both practical and theoretical advances in the observation and exploitation of the apparent scintillations of radio sources due to their radiation impinging upon plasma. This led him to propose, and secure funding for, the construction of the Interplanetary Scintillation Array, a large array radio telescope at the Mullard Radio Astronomy Observatory (MRAO), Cambridge to conduct a high time-resolution radio survey of interplanetary scintillation.
Hewish was professor of radio astronomy at the Cavendish Laboratory from 1971 to 1989, and head of the MRAO from 1982 to 1988. He developed an association with the Royal Institution in London when it was directed by Sir Lawrence Bragg. In 1965 he was invited to co-deliver the Royal Institution Christmas Lecture on Exploration of the Universe. He subsequently gave several Friday Evening Discourses and was made a Professor of the Royal Institution in 1977. Hewish is a Fellow of Churchill College, Cambridge. He is also a member of the Advisory Council for the Campaign for Science and Engineering.
One of his PhD students, Jocelyn Bell, noted the radio source which was ultimately recognised as the first pulsar. The paper announcing the discovery had five authors, Hewish's name being listed first, Bell's second. Hewish and Martin Ryle were awarded the Nobel Prize in Physics in 1974 for work on the development of radio aperture synthesis and its role in the discovery of pulsars. The Nobel award to Ryle and Hewish without the inclusion of Bell as a co-recipient was controversial, and was roundly condemned by Hewish's fellow Astronomer Fred Hoyle. See Nobel prize controversies.