He was brought up in Surrey and London, and educated at Westminster School and New College, Oxford. Aged 16, he travelled to Italy to meet Ezra Pound, and he was still a teenager when he launched Agenda in the late 1950s.
On Cookson's death a "Celebratory Issue" of Agenda (Vol. 39, No. 4 (2003)) was published in which his successor as editor of the journal, Patricia McCarthy, described him as "a man who sacrificed his life for poetry and was perhaps the best, most single-minded editor of our day". In addition to a final redaction of "Vestiges and Versions", the issue contains biographical sketches by Edmund Gray and Martin Dodsworth.
- A Guide to The Cantos of Ezra Pound (1985; Revised Edition, 2001)
- (Note: An Introduction to David Jones was announced but not seemingly published.)
- Ezra Pound: Selected Prose 1909-1965 (Faber, 1973)
- Agenda - An Anthology 1959-1993 (Carcanet Press, 1994)
- Dream Traces (Hippopotamus Press, 1975)
- Spell (Agenda Editions, 1986)
- Vestiges (Agenda Editions/Big Little Poems, 1987)
- Vestiges & Versions 1955-1996 (Agenda Editions/Poet and Painters Press, 1997)