Runcorn was born at Southport in Lancashire, and was educated at Cambridge University. After working on radar during World War II he held teaching appointments at the University of Manchester (1946–50) and at Cambridge (1950–55), before being appointed in 1956 to the chair of physics at King's College, Newcastle, which became the University of Newcastle upon Tyne in 1963. He became Senior Research Fellow at Imperial College, London, in 1989.

Under the early influence of Patrick Blackett, Runcorn began research on geomagnetism. From detailed field surveys in both Europe and America they were eventually able to reconstruct the movements of the North Magnetic Pole over the past 600 million years. Runcorn found that he obtained different routes for the migration depending on whether he used European or American rocks. Also, the European rocks always pointed to a position to the east of that indicated by the American rocks for the magnetic pole. From this evidence Runcorn argued, in his paper Paleomagnetic Evidence for Continental Drift (1962), that if the two continents were brought close to each other they could be so aligned that the magnetic evidence of their rocks pointed to a single path taken by the magnetic pole. This led Runcorn to become an early supporter of the newly emerging theory of continental drift.

Runcorn died in somewhat mysterious circumstances: he was found battered to death in a motel room in Los Angeles, where he had been attending a conference.