Born to an upper-middle-class family, Coldstream was educated at Rugby School and Oriel College, Oxford, where he read law.

After retirement on 5 April 1968, Coldstream continued to advise the government, and served as chairman of the Council of Legal Education from 1970 to 1973.

After gaining a second class honours in Jurisprudence he left in 1929, planning to become a barrister, and was called to the Bar by Lincoln's Inn in November 1930.

Coldstream started his career practising as a barrister, but after four years was hired by the Office of the Parliamentary Counsel, the civil service body tasked with drafting Bills for the Parliament of the United Kingdom.

[3] Between 1944 and 1946 he served as a member of the British War Crimes Executive, preparing files for the Nuremberg Trials in which he played a significant role, and from 1947 to 1953 he sat on the Evershed Committee.

[3] As Permanent Secretary Coldstream served with distinction, and played a part in some of the most important reforms of his era, as well as executing his normal duties.