Barrett's first post was as a lecturer at Christ Church, Oxford, from 1938 to 1939, and then at
Keble College, Oxford, where he was a Lecturer from 1939 to 1952 and Tutor in Classics from 1939 to 1981. At Keble, he was also the college's Librarian from 1946 to 1966, a
Fellow of the college from 1952 to 1981 (and Honorary Fellow, from 1981 until his death), and Sub Warden, 1968 to 1976. At the University level, he was lecturer in Greek Literature, 1947 to 1966, and then Reader in Greek Literature until 1981. Barrett's edition of
Euripides' tragedy
Hippolytus appeared in 1964 and was recognised as one of the most important works on Greek tragedy. At his death, Barrett left a major work on
Pindar unpublished. When an
Inland Revenue tax inspector once challenged his tax return, questioning whether a computer was an allowable expense for a classicist, Barrett was able to show that for an understanding of the text of Pindar it was essential to know how
Mount Etna had appeared to a sailor passing the mountain in a ship. The distinction of Barrett's scholarship was recognised by a fellowship of the
British Academy. ==War service==