Alistair Bevington was born in London, England in 1926 and studied at Cambridge University in Cambridge, England and at the Architectural Association in London. Subsequent research on concrete while with the Housing Section of London County Council led to experiments with slab glass in concrete at the studio of Council's Central School of Arts and Crafts where he met a fellow student, Mariette Glover.
Following their marriage in 1956 the Bevingtons moved to Yonkers, New York, where Alistair Bevington continued to practice as an architect. He was employed for two years by the firm of Philip Johnson Associates on the new Seagram building in New York City. He also worked for a number of years with the architect Edward L. Barnes.
In addition to his architectural activities, Alistair Bevington also worked as a sculptor and stained glass designer, often in collaboration with his wife. Their commissions included constructions for offices and apartments. In 1968 Alistair Bevington designed a sundial for the dormitory courtyard of the campus of Rochester Institute of Technology in Rochester, New York.