He joined the civil service at age 16, and during World War II was seconded to a radar development project.
[1] He did his graduate studies in mathematics at King's College London under the supervision of Anthony Francis Ruston, on subjects related to the Hahn–Banach theorem.
In 1966 he took up a Chair in Pure Mathematics at Cardiff University, but he returned to Oxford in 1967, becoming a fellow of Balliol College, where he remained for the rest of his career.
In his work Ingleton studied matroids as a generalization of the concept of linear independence.
He included in his paper a single theorem giving a necessary condition for the representability of matroids.