Wraith was born in Derbyshire; his father worked for the Midland Railway. He studied economics at University of Birmingham. He spent two years in Australia and New Zealand before becoming the warden at a Tyneside community center managed by the Tyneside Council of Social Services when the worst of the Great Depression was over. In 1938, he joined the Education Department of the Borough of Southampton as the Secretary of Youth Services and served in the position through World War II. In 1945, he was the head of the London School of Economics's department involved in colonial studies, also known as the Colonial Social Science Certificate Course that was previously headed by Audrey Richards. In 1946, he visited Africa and worked with the Housing and Social Services Department of Gold Coast. In 1947, he was placed in charge of another course, the Post War Devonshire Courses for colonial and West African administrators. Wraith later published a book on local government, comparing the West African and the English local government systems and expressing doubt about the transferability of the English model to West Africa.