William Clarke was born on 22 May 1883, the son of the solicitor-general Sir Edward George Clarke and his wife, Kathleen Mathilda Bryant. He was the youngest of three children and the only child of his father's second marriage. Educated at Harrow School and Magdalen College, Oxford (1902-5), Clarke was called to the bar in 1906. On 31 July 1907 he married Dorothy Mainland: they had one son and two daughters.

When war broke out, Clarke left the law for the Navy. In February 1915 he was commissioned as an assistant paymaster (later promoted to paymaster lieutenant-commander). Then in early 1916 the director of naval intelligence, Captain [William] Reginald Hall, recruited him into the new code-breaking unit Room 40. Clarke was particularly good at analysing information, and together with his colleague Frank Birch, he was selected to write a history of Room 40. However, due to Clarke's rather outspoken approach, the history was never published.

In 1919 Clarke joined the Government Code and Cypher School (GCCS), the successor to Room 40 and its War Office counterpart. In 1924 he made a return to more specifically naval work when he was promoted to head the new naval section within the GCCS, a post which Clarke retained until 1941. The GCCS moved to Bletchley Park during the Second World War and Clarke had an important role in the successful decryption of the German and Italian (Enigma) machine codes, particularly devoting himself to Italian naval codes, 1939-40. He retired after the war in October 1945 and died on 5 February 1961.