 Ackrill was born, to Frederick William Ackrill and Jessie Anne Ackril, in Reading, Berkshire where he attended Reading School.In 1940 he entered St. John's College, Oxford as a scholar in Classics where his philosophy tutors were Paul Grice and John Mabbott.The next year he left for war service in the Royal Berkshire Regiment and General Staff, reaching the rank of captain.He returned to Oxford in 1945 to read "Literae Humaniore", graduating in 1948.