Crozier was born in London, and after an apprenticeship at the Old Vic theatre, he joined the Sadlers Wells Opera Company in London during the Second World War, and directed Britten's first opera, Peter Grimes, at Sadler's Wells in 1945. He founded the English Opera Group in 1947, and co-founded (with Britten) the Aldeburgh Festival in 1948. He directed his second wife, Nancy Evans, in the role of Lucretia in the 1946 premiere of Britten's opera The Rape of Lucretia at Glyndebourne, and later succeeded Peter Pears as director of the Aldeburgh Festival. He was appointed OBE in the 1991 New Year Honours.
Eric Crozier's first opera libretto for Britten was Albert Herring (1947), and he later wrote and/or directed several other Britten operas. Crozier's and Nancy Evans' archives are preserved at Aldeburgh. He died at Granville, France.