He was elected a Fellow of All Souls College, Oxford for the seven-year period 1952-59. He spent the academic year 1953-54 studying at Westcott House, Cambridge and he was ordained deacon in 1954. He served as a tutor at Westcott House 1954-55 and he was ordained priest in 1955.
In 1955 he started his pastoral ministry as Assistant Curate of Hampstead St John and he began his work with the Student Christian Movement as Secretary, remaining in both posts until 1958.
He was Assistant Curate of St Martin-in-the-Fields 1958-66, editor for the Student Christian Movement Press 1959-66, and General Secretary of the Student Christian Movement 1965-66.
From 1966 until 1970 he was Dean of King's College, Cambridge. He was a Six Preacher of Canterbury Cathedral 1969-76.
He was a Canon of Westminster Abbey and Rector of Westminster St Margaret 1970-78. He was additionally Chaplain to the Speaker of the House of Commons 1972-78 and Sub-Dean of the Abbey 1974-78. He was Chairman of the Churches' Council on Gambling 1970-78 and of Christian Aid 1971-78.
He was Dean of Norwich 1978-83 and Provost of Southwark 1983-94.
He retired to Winchester, becoming Honorary Chaplain at Winchester Cathedral in 1995.
In 1990 the Archbishop of Canterbury, Robert Runcie, conferred upon him the degree of Doctor of Divinity. He wore the academic dress of his former headmaster, Fred Shirley, who had himself been a Doctor of Divinity, and of whom Edwards wrote a biography, F. J. Shirley: An Extraordinary Headmaster (London: SPCK, 1969).
In the same year he was appointed an Honorary Fellow of South Bank Polytechnic (later South Bank University and now called London South Bank University).
In 1995 HM the Queen appointed him an Officer of the Most Excellent Order of the British Empire.