Buxton was educated at
Rugby School and
Trinity College, Cambridge, where he graduated with first class honours in Natural Sciences, in 1915. He was elected a fellow of the college in 1916. He continued his studies at
St George's Hospital, London and qualified in medicine in 1917. Since it was during the
First World War, he immediately took up a commission in the
Royal Army Medical Corps and served in
Mesopotamia and North West
Persia. While in the middle east he extensively collected and developed his interest in insects. In 1921, Buxton accepted the post of an entomologist in the Medical Department in
Palestine. From 1923 to January 1926, he was on a collecting expedition in
Samoa. On returning to London, he was appointed head of the Department of Entomology in the
London School of Hygiene and Tropical Medicine. His work was mainly focused on understanding insects in relation to control. He was involved in the practical control of pests such as lice, mosquitoes, and flies during the
Second World War. After the war in 1945–1946, he was involved in East Africa on the problem of the control of
Tsetse flies. ==Awards and honours==