Haldane was born in Edinburgh to Mary Elizabeth Burdon-Sanderson and Robert Haldane. His grandfather was the evangelist James Alexander Haldane. His mother was the daughter of Richard Burdon-Sanderson and the granddaughter of Sir Thomas Burdon. His maternal uncle was the physiologist John Scott Burdon-Sanderson. He was the brother of Elizabeth Haldane, John Scott Haldane and Richard Burdon Haldane, 1st Viscount Haldane.
- Thomas Graeme Nelson Haldane (1897–1981)
- Archibald Richard Burdon Haldane (1900–1982)
- Mary Elizabeth Campbell-Fraser (1895–1983)
- "Obituary: Sir William Haldane". The Times. The Times Digital Archive. 8 November 1951. p. 8.
- Scotland, Select Births and Baptisms, 1564-1950