In 1958 Brian Cox (C.B., "Brian" or "Charles") and A.E. ("Tony") Dyson established the Critical Quarterly, initially based at the University of Hull where Cox was a lecturer. Cox and Dyson served as editors, and their literary journal aimed to promote English literature from the medieval to the modern period. The journal placed a particular emphasis on contemporary poetry and included writings by British, American, Canadian, Irish, and Australian authors of the 20th century, many of whom became famous poets and authors. These included Sylvia Plath, Philip Larkin, Anne Sexton, and R.S. Thomas. The journal also published established authors, such as W.H. Auden.

The journal had a large audience from the outset, averaging 5,000 subscriptions until the early 1970s. Colin MacCabe took over as general editor of the journal in 1989, which continues to be published.