Cochrane was born, and brought up in Greenock, Scotland. He left school at an early age to work to support his widowed mother and the younger children of the family. Listening to D. L. Moody in 1882 brought him to a strong evangelical faith, which determined the rest of his life. In the face of great difficulties, he trained as a doctor in Glasgow and offered himself for service with the London Missionary Society (LMS), requesting appointment "where the work was most abundant and the workers fewest." In 1897 the LMS appointed him and his wife to Chaoyang, Liaoning Province, in northern China to take up the work James Gilmore had begun.
Conditions there, including the desperate shortage of trained personnel, medical equipment, and supplies, made a deep impression. He survived the Boxer Rebellion, and in its aftermath the LMS appointed him to rebuild its hospital in Peking (Beijing). Out of his vision and through his diplomatic skills, the Peking Union Medical College was born, with support from other mission bodies and the empress dowager, and he became the college's first principal. Its high standards were recognized throughout China and beyond, and in 1915 he negotiated the underwriting of its financial needs by the Rockefeller Foundation.
From his China experience grew his lifelong concern for the best use of the available resources for mission and the need of cooperation to achieve this. In 1913 the Christian Literature Society of China published his Survey of the Missionary Occupation of China with an accompanying Atlas of China in Provinces Showing Missionary Occupation.
After his return to England in 1915, Cochrane served at the headquarters of the LMS and also with the National Laymen's Missionary Movement. In 1918 a Survey Trust was formed with Cochrane, Roland Allen and Sidney J. W. Clark (a wealthy Congregationalist businessman with a life long commitment to world mission) as its three trustees. In 1920, in conjunction with Roland Allen, Cochrane published Missionary Survey as an Aid to Intelligent Co-operation in Foreign Mission, and in 1924 the Survey Application Trust was formed. Although "Survey" featured prominently in both the name and activities of the trust, the deed specifically charged the trustees to promote and apply, anywhere in the world, the principles asserted by Clark in his pamphlets and Allen in his two principal books, Mission Methods: St. Paul's or Ours? and The Spontaneous Expansion of the Church. The World Dominion Press was the publishing branch of the trust, and a list of its publications indicates how it sought to fulfill this dual function of survey and die promotion of indigenous principles.
In all of this survey work, Cochrane's managerial skills and ability to reconcile those of different traditions were at work. The compiling of the first edition of the World Christian Handbook, issued in 1949, edited by E. J. Bingle and K. G. Grubb, fulfilled one of Cochrane's long-standing ambitions. In another direction, he purchased the Mildmay Centre in London in 1931 as a base for the Movement for World Evangelization, with the task of mission on its doorstep, which exemplified his combination of vision and broad evangelical concern. He died in Pinner, Middlesex.