Woods was a leading supporter within the Militant tendency within the Labour Party and its parent group the Committee for a Workers' International until the early 1990s.

[5] Woods was born into a working-class family in Swansea, South Wales and grew up in the Townhill and Penlan areas of the city.

[2] At the age of 16 he joined the Young Socialists and became a Marxist, becoming a supporter of the Trotskyist Militant tendency within the Labour Party.

[8] In the early 1990s, Woods and his mentor, Ted Grant, left the Militant tendency and its parent organization, the Committee for a Workers' International, over what they considered to be the ultraleft turn of this organisation when it decided to split from the Labour Party.

[citation needed] The minority group, led by Ted Grant, also argued that a decline in emphasis on political education, as well as the development of a bureaucratic clique around Peter Taaffe, was damaging Militant.