Perrin was born in Wellingborough, Northamptonshire, England, and served from 1940 to 1945, during the Second World War, in the Royal Air Force.
He earned a Bachelor of Arts degree (in theology) in 1949 from the Victoria University of Manchester.
In 1952, he earned a Bachelor of Divinity degree (with honours), and in 1956 a Master of Theology (in Greek New Testament and apocryphal studies), both from the University of London.
Perrin was granted his Doctorate of Theology from the University of Göttingen in 1959.
From 1959 to 1964, he taught New Testament at the Candler School of Theology, Emory University, and from 1964 until his death in 1976 at the Divinity School of the University of Chicago.