Blackham was born in West Bromwich, Staffordshire, on 31 March 1903. Blackham left school following the end of World War I, and became a farm labourer, before gaining a place at Birmingham University to study divinity and history.[2] He acquired a teaching diploma and was the divinity master at Doncaster Grammar School.
Joining the Ethical Union, Blackham drew the organisation further away from religious forms and played an important part in its formation into the British Humanist Association, becoming the BHA's first Executive Director in 1963. He was also a founding member of the International Humanist and Ethical Union (IHEU), IHEU secretary (1952–1966), and received the IHEU's International Humanist Award in 1974, and the Special Award for Service to World Humanism in 1978. In addition he was one of the signatories to the Humanist Manifesto.