Stewart was born in Glasgow but brought up in London where he attended Colfe's Grammar School (1927-34) and University College, London (1934-8) where he obtained a BA degree in English. He obtained a PhD in 1947 from the University of London on which he later based a book, The Quakers and Education.
He was housemaster at the Friends School, Saffron Walden from 1938-43 and then moved to Abbotsholme School, Derbyshire from 1943-44. He lectured in education at University College, Nottingham (now the University of Nottingham) and at the University of Wales in Cardiff from 1944-50. In 1950 Lord Lindsay, the founder of the newly opened University College of North Staffordshire, (now Keele University), appointed him the Chair of Education in 1950. At Keele he built up the department and later the Institute of Education. He became Acting Principal at Keele after the death of Sir George Barnes in 1960. In fact Keele's first three principals had all died in office.
In 1947 he married Elizabeth (Ella) Burnett, a practising Quaker, and had one son and one daughter. In 1954 he contracted polio, which left him with a permanently paralysed left arm. He died following a car accident on a return visit to Keele. His funeral was held in the university chapel.