 Postgate was educated at the private Woodstock School on Golders Green Road in Finchley in north-west London and Woodhouse Secondary School, formerly known from 1923 onwards as Woodhouse Grammar School, also in Finchley (and now renamed Woodhouse College), followed by Dartington Hall School, a progressive private boarding school in Devon.Postgate joined the Home Guard in 1942 while studying at the Kingston School of Art, but when he became liable for military service during the Second World War the following year, he declared himself a conscientious objector, as his father had done during the First World War.He was initially refused recognition; he accepted a medical examination as a first step to call up, and then reported for duty with the Army in Windsor, but refused to put on the uniform.