Educated at Edinburgh Academy and the University of Edinburgh where he gained a BSc in Agriculture, Murray went into employment with the Ministry of Agriculture from 1925 to 1926. He was then awarded a Commonwealth Fund Fellowship, and spent three years at Cornell University working towards a PhD.
It was in 1929 that Murray first went up to Oxford, attending Oriel College and the Agricultural Economics Research Institute until 1932. He became a Research Officer for the AERI, a post he held until 1944. In 1937, however, he was appointed a Fellow and Bursar of Lincoln College, as well as being appointed by the University to Oxford City Council. On the death of Rector Munro in 1944, he was elected to the Rectorship, a position he held until his retirement in 1953. He became the first Rector since Nathaniel Crew not to die in office.
In 1957, Sir Robert Menzies, the Australian Prime Minister, asked him to serve on the Committee on Australian Universities. He went on to hold the positions of Vice President of Wellington College (1966-69), Honorary President of the National Union of Students (1967-70), Chairman of the Committee of Enquiry into the Governance of the University of London (1970-72) and Chairman of the Royal Commission for the Exhibition of 1851 (1962-71).
He held honorary Fellowships of Downing College, Cambridge; Oriel College, Oxford; Birkbeck College, London; and Lincoln College, Oxford. In 1964, he was created a life peer as Baron Murray of Newhaven, of Newhaven in the County and City of Edinburgh.