Born in Paisley on 29 October 1882, he was the eldest child of George Hanna Cockburn (a schoolmaster) and Isabella Brodie Marshall.[1] After receiving his school education in Paisley, he studied at the University of Glasgow, graduating in Arts and Divinity.[1]
In 1908 he was ordained in Mearns parish; in 1914 he was translated to Battlefield parish, Glasgow.[1] He married Amy Macloy, daughter of another minister, in 1912, who would in time bear him a son and daughter.[1] During World War I he was a British army chaplain, serving in France, Egypt and East Africa.[1]
After the war, he returned to Scotland, where on 8 May 1918, he became minister at Dunblane Cathedral.[1] In the following years he served as the convener of the Business Committee of the General Assembly of the Church of Scotland, and was convener of the Committees on Church and Nation and Inter-Church Relations, and was clerk to the committee from 1927 until 1929, promoting union between the Church of Scotland and the United Free Church.[1]
In 1944, he became a Chaplain to King George VI,[2] and retained such a position after the accession of his daughter Elizabeth II in 1952.[1] When he died in 1973, he was Senior Extra-Chaplain to the Queen.[1]
Cockburn departed Dunblane in 1945 for Geneva, taking the position of Director of the Department of Reconstruction and Inter-Church Aid of the World Council of Churches.[1] From 1952 until 1954 he was a member of the Royal Commission on Scottish Affairs.[1]
In 1930, he was one of the founders of the Society of Friends of Dunblane Cathedral, whose journal he edited between 1930 and 1965.[3] He created a museum for the church in the Dean's House, and used his connections to acquire material to fill it.[3] Cockburn contributed many articles for this journal.[3] Cockburn also published several books on religious history:
The Celtic Church in Dunblane : a View of the Scottish Church from S. Ninian to the Culdees and the coming of the Roman Catholic Church, Dunblane: Society of Friends of Dunblane Cathedral, 1954
Religious Freedom in Eastern Europe, Richmond, Virginia: John Knox Press, 1953
The Medieval Bishops of Dunblane and their Church, Dunblane: Society of Friends of Dunblane Cathedral, 1959
Bowser, D. C. (1973), "James Hutchison Cockburn", Journal of the Society of Friends of Dunblane Cathedral, 11 (Part iv), Dunblane: Society of Friends of Dunblane Cathedral: 100–2.