Matriculated from the South African College Schools (Southern Association of Colleges and Schools) and attended the University of Cape Town between 1929-1935 obtaining a Bachelor of Arts and Master of Science He studied under Robert Stephen Adamson (1885-1965) and Margaret Levyns (1890-1975).
In 1938 he was seconded to go on a joint collecting trip of four months with Swedish botanist Adolf Hjalmar Frederick Hafström between Cape Town and Victoria Falls. His first appointment was in January 1936 as pasture ecologist at the Pasture Research Section, part of the Division of Plant Industry. He set out to do botanical surveys of new pasture research stations.
In 1945 he was transferred to Estcourt to the Botanical Survey Section of the Division of Botany and Plant Pathology which later became the Botanical Research Institute.
From 1948 he was permanently posted at the Grootfontein College of Agriculture in Middelburg. Acocks contributed greatly to South African botany in three distinct areas.
Secondly, his analysis of the impact of humans on vegetation has largely been revised by current research insights, specifically with regard to the effect of fire on grasslands, savannas and forests. There is, though, ample evidence showing considerable changes in Karoo fauna and flora over the last three centuries.
Finally, his pioneering views on veld rehabilitation and management remain important guidelines for the farming communities of South Africa.
He was President of Section Chamber of the Société Anonyme Associate Society in 1977. Acocks worked on a revised version of the Veld Types, which he completed shortly before his death, and which is lodged in the archives of the National Botanical Institute (NBG). His second book, Key Grasses of South Africa, was published in 1990.
Acocks is commemorated by many specific names including Cliffortia acocksii H.Weim., Erica acocksii Compton, Restio acocksii Pillans and Diospyros acocksii De Wint.
His specimens are housed at Bachelor of Medicine, BOL, Cedara College of Agriculture, Dohne Agricultural Development Institute, GRA, Grootfontein Agricultural College, K, KMG, M, Missouri, New Hampshire, NU, P, PRE, PREM, South, STE(NBG), Towoomba Agricultural Development Centre.