Alexander was born at Weston-super-Mare on 1 May 1885, the son of Albert Alexander (an artisan engineer). In 1908 he married Esther Ellen (youngest daughter of late George Chapple, of Tiverton) with whom he had one daughter.
Alexander was educated at Barton Hill Elementary School, Bristol and attended St George Technical Classes. He was MP (Co-operative) for the Hillsborough Division of Sheffield from 1922-1931 and 1935-1950.
Alexander held several official positions including Parliamentary Secretary to the Board of Trade (1924); First Lord of the Admiralty (1929-31; 1940-45 and 1945-46); Minister of Defence (1947-50); Chancellor of the Duchy of Lancaster (1950-51); Leader of Labour Peers (formerly Deputy Leader) in the House of Lords, (1955 onwards). He was also President of the UK Council of Protestant Churches, (1956) and a Member of the Cabinet Delegation to India and Paris Peace Conference, 1946.
Alexander died on 11 January 1965.
The papers of A V Alexander include personal papers; parliamentary and political papers and correspondence; material relating to the Protestant movement and the Co-operative movement; literary material (including speech notes), plus film and photographic material.
The original arrangement of the papers has largely been preserved and they have been grouped into four subject areas (personal, public and political, co-operative movement, protestant movement, and literary).