Drewry was educated at Havelock Grammar School (now the Havelock Academy) in Grimsby. He then studied at Queen Mary College in east London, graduating with a Bachelor of Science in Geography in 1969. He then studied in Cambridge, residing at Emmanuel College, Cambridge, and completed a Doctor of Philosophy on Glaciology and Geophysics in 1974 with thesis titled Sub-ice relief and geology of East Antarctica.
Since 1 July 2015 he is the Vice-President of the European University Association. From 1978 to 1983, Drewry was a Senior Research Assistant at the Scott Polar Research Institute, and then Assistant Director of Research in 1983. He was Director of the Scott Polar Research Institute from 1984 to 1987, and then Director of the British Antarctic Survey from 1987 to 1994.
He is an Honorary Fellow of Emmanuel College, Cambridge.
He became the Vice-Chancellor Designate of the University of Hull in November 1999, being designated to take over on the planned retirement of the previous incumbent, David Dilks, in January 2000. On 1 September 2009, he was succeeded by Calie Pistorius, formerly the Vice-Chancellor of the University of Pretoria.
Drewry has received several awards and honours for his work. Polar Medal (United Kingdom) Antarctica Service Medal (United States of America) 1994 - Prix de la Belgica Gold Medal of the Royal Belgian Academy of Sciences 1998 - Patron"s Medal of the Royal Geographical Society Drewry Ice Stream in Ellsworth Land and Mount Drewry in the Queen Alexandra Range are named after him.
