Alice Rosemary Murray was born in Havant, Hampshire, on July 28th 1913, the daughter of Admiral Arthur John Layard Murray and Ellen Maxwell Spooner (daughter of Dr William Spooner, Warden of New College, Oxford). She inherited their belief in the equality of the sexes, exemplified in the way in which they raised their six children. After gaining a B.A. in chemistry at Lady Margaret Hall, Oxford, in 1935, followed by a D.Phil., 1938, Rosemary Murray held teaching posts at Royal Holloway, London (1938-41), and Sheffield University (1941-42). In 1942 she entered the WRNS as a rating, finishing in 1946 as a Chief Officer at Chatham, dealing with the demobilization of thousands of Wrens. This was a formative period in her life. She then moved to Cambridge as a lecturer at Girton College and Demonstrator in the Department of Chemistry. Her Girton career spanned 1946 to 1954: a lecturer from 1946-54, a Fellow from 1948-54, and a Tutor from 1951-54, she was also made an Honorary Fellow of Girton College in 1975.

In Cambridge, Rosemary Murray became an active member of the Third Foundation Association, which established New Hall as the third college for women. She became Tutor in Charge and lead the new institution with the assistance of Miss Robin Hammond. New Hall began in 1954 with sixteen students in a converted guest house. Rosemary Murray managed the admission and direction of students and made the day-to-day decisions which would establish the character of the embryo college. She also acted as handyman, gardener, and boatkeeper, whilst keeping in sight the goal of achieving permanence for New Hall as a full college of the University.

She oversaw the setting and marking of New Hall's innovative examination paper, and the interviewing of candidates. Her aim was to widen access to all bright girls, regardless of background and schooling. Some found her austere, but those who penetrated her reserve found her the kindest of women, and a wonderful teacher.

The New Hall endowment appeal took off slowly, but crucially a gift of land on Huntingdon Road in Cambridge was received from descendants of Charles Darwin. The architects Chamberlin, Powell and Bon were appointed in 1959 and large donations came from the Wolfson and Elizabeth Nuffield Foundations. From 1962 onwards she oversaw every detail of the plans and made some important contributions to the design of the new buildings. She was designated the college's first President in 1964 and was still in post to celebrate the College’s Silver Jubilee, retiring in 1981.

When New Hall achieved its royal charter and became a full college in 1972, its President became eligible to be Vice-Chancellor of the University. Rosemary Murray was not only the first woman to hold the position (from 1975 to 1977) but also the first head of a modern college to do so, and only the second woman to be vice-chancellor of a British university.

In the world outside the University Dame Rosemary held many other responsible positions. She was a JP for thirty years; she served on the Lockwood Committee which recommended a second university for Northern Ireland and on the Armed Forces Pay Review Board; she was also a director of the Observer and chair of the governors of Keswick Hall, which later became part of the University of East Anglia. Significant breakthroughs were as the first woman director of a clearing bank (the Midland), the first woman liveryman, in the Goldsmiths’ Company, and the first woman Deputy Lieutenant for Cambridgeshire. She received honorary degrees from five British and three American universities and was appointed DBE in 1977. She died in Oxford on October 7th, 2004, almost exactly 50 years to the day since the establishment of New Hall.