By virtue of his position as Archbishop of Westminster, Murphy-O'Connor was sometimes referred to as the Catholic Primate of England and Wales. However, though the holders within the Church of England of the posts of Archbishop of Canterbury and Archbishop of York are called the "Primate of All England" and "Primate of England" respectively, the title of primate has never been used by the de facto leaders of the Catholic Church in England and Wales.
Cormac Murphy-O'Connor was born on 24 August 1932 in Reading, Berkshire, the fifth son of George Murphy-O'Connor, a G.P., and Ellen (née Cuddigan; died 1971), who emigrated from County Cork in Ireland before the First World War and married in 1921. The Murphy-O'Connor family was middle class, with the men becoming doctors or priests, and one in each generation taking over the family business as wine merchants 'to the clergy and gentry of Southern Ireland'. A forebear, Daniel Murphy, became the first Archbishop of Hobart, Tasmania, in 1888, having served as a bishop there since 1865. Two of his uncles, one aunt, two cousins and two of his brothers, Brian (1930–2012) and Patrick, were also ordained or members of religious orders. His youngest brother, John, was a regular officer in the Royal Artillery who died of renal cell carcinoma; he had two other siblings, James (a doctor and rugby player) and Catherine. His cousin, Jerome Murphy-O'Connor, was a Dominican priest and expert on St Paul who served as Professor of New Testament at the École Biblique in Jerusalem from 1967 to his death in 2013. After attending Presentation College in Reading and Prior Park College in Bath, in 1950 Murphy-O'Connor followed his brother Brian to the Venerable English College in Rome and began his studies for the priesthood, where he received a degree in theology. Thereafter, he earned a licentiate in philosophy and a Licentiate of Sacred Theology degree from the Pontifical Gregorian University. He was ordained on 28 October 1956, by Cardinal Valerio Valeri. For the next decade he was engaged in pastoral ministry in Portsmouth and Fareham.
In 1966, Murphy-O'Connor became the private secretary to Bishop Derek Worlock of Portsmouth. In September 1970, he was appointed parish priest of the Immaculate Conception church in Portswood, Southampton. Soon afterwards, in late 1971, he was appointed rector of the Venerable English College, his alma mater. As rector he hosted the Anglican Archbishop of Canterbury, Donald Coggan, on his historic visit to Pope Paul VI in 1977.
On 17 November 1977, Murphy-O'Connor was named Bishop of Arundel and Brighton by Pope Paul VI. He received his episcopal consecration on the following 21 December from Bishop Michael Bowen, with Archbishop George Dwyer and Bishop Anthony Emery serving as co-consecrators. He held important positions among the bishops of Europe and has also been consistently influential in ecumenical work; from 1982 to 2000 he was Co-Chairman of the Anglican–Roman Catholic International Commission. In 2000 he was awarded the Lambeth degree of Doctor of Divinity by the Archbishop of Canterbury, George Carey, in recognition of his work for Christian unity.
Murphy-O'Connor was appointed the tenth Archbishop of Westminster, and thus head of the Catholic Church in England and Wales, on 15 February 2000; in November of that year he was elected President of the Catholic Bishops' Conference of England and Wales.