She was born in Bury, Lancashire, and educated at the School of S. Anne, Abbots Bromley and St Hugh's College, Oxford.  After completing her Oxford degree she became an Assistant Lecturer in History at the University of Sheffield in 1917.  In 1922, as a result of illness, she took a year’s leave which she spent in Somaliland with her sister’s family, beginning her lifelong interest in the British African colonies.
In 1924 she became a Tutor and subsequently Fellow in Modern History and Modern Greats (philosophy, politics and economics) at St Hugh’s College. In 1929 she was awarded a Rhodes Scholarship, and from July 1929 until early 1932 visited the United States, the Pacific islands, Australia, New Zealand, and much of Africa south of the Sahara. In 1932 she was awarded a Rockefeller Travelling Fellowship for travel and study in East Africa and the Sudan.  During the 1930s she wrote the first of many books on Africa, including Native Administration in Nigeria (1937) and African Discovery (1942; jointly with Jack Simmons), and from 1935 to 1939 was Research Lecturer in Colonial Administration at Oxford.  In 1939 she was appointed the first official and only woman fellow of the newly founded Nuffield College, Oxford, and was also elected Reader in Colonial Administration, a post she held until 1948. Her teaching at this time was almost entirely devoted to the first and second Devonshire courses for colonial servants, though later she played a part in the development of universities for the new African leaders and experts, and helped in the initiation of the Oxford Colonial Records Project. Her books, reports and papers provided the basis for the Oxford Institute of Colonial Studies, to which she was appointed Director, 1945-1948. 
Her official biography of Lord Lugard appeared in two volumes in 1956 and 1960, and she published four volumes of Lugard’s diaries (1959–63).
In 1961 she became the first woman to deliver the Reith Lectures, her lectures being published as The Colonial Reckoning .
She was appointed CBE in 1948 and DCMG in 1965. She received honorary degrees from several universities, and was made an Honorary Fellow of St Hugh’s College, Oxford, in 1962.  She was the first President of the African Studies Association of the UK (ASAUK; 1963-64).
In 1968 she was criticised strongly when she espoused the cause of Biafra in the Nigerian Civil War. After a visit to Nigeria she recanted her earlier views publicly on radio and television. She was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 1969.