[2][3] Born in Norwich and educated at Downing College, Cambridge, Clapham worked at Rothamsted Experimental Station as a crop physiologist (1928–30), and then took a teaching post in the botany department at Oxford University.
He received a BA with First Class Honours and was awarded the Frank Smart Prize for Botany.
[1] After completing his B.A., Clapham did graduate work in plant physiology under the supervision of Frederick Blackman before taking up a position as crop physiologist at the Rothamsted Agricultural Experimental Station where he worked with Ronald Fisher.
[1] It was during this time period that he met his future wife, Brenda Stoessiger who was a research student working with Karl Pearson,[1] a pioneer of mathematical statistics.
In 1944 he left Oxford to take up the position of Chair of Botany at the University of Sheffield where he remained until his retirement in 1969.
Clapham received the Linnean Medal in 1972, and was appointed Commander of the Order of the British Empire in 1969.
Beginning in 1940, Clapham took a lead role in the production of the ongoing Biological Flora of the British Isles.