Born and raised in Hackney, the son of a cabinet maker, and influenced by the deprivation of the East End of London he joined the Communist Party as a founder member in 1920.

In 1921 Woolf gained a place at Sidney Sussex College, Cambridge, something that would have been unaffordable without a full scholarship, to read for the Natural Science Tripos, and graduated in 1924 with a double first.

His proposers were Francis Albert Eley Crew, James Gray Kyd, Lancelot Hogben and John Du Plessis Langrishe.

His FRSE obituary[3] notes that 'Woolf's 1951 paper on "Computation and interpretation of multiple regression" is a model of clarity of exposition and was to become very widely used.

Woolf was a considerable wit and the lyricist of satirical songs on politics for Unity Theatre in the late 1930s and early 40s, many with melodies by the American Big Band leader Van Phillips.

[9] The best known of these is " Pity the Downtrodden Landlord,"[10] which has been recorded by, among others, The Weavers, Alfie Bass, Stan Kelly, Oscar Brand and Fred Hellerman,[11] and was published in America in 1948 in 'The People's Songbook'.

[12] The editors noted that the song 'was caught up by thousands of United States tenants threatened with eviction when Congress lifted rent controls.'

In the 1960s Woolf wrote the book and Van Phillips the score for the musical 'Skerryvore', based on a play by James Bridie about a fictional Scottish University, which was performed on both the amateur and professional stage in Scotland in the 1960s and 70s.

Woolf also set songs on scientific life to popular tunes for his colleagues in the genetics department of Edinburgh University.