The son of Arthur Greenwood (Deputy Leader of the Labour Party under Clement Attlee) and his wife Catherine Ainsworth, Greenwood was born in Leeds[1] and educated at Merchant Taylors' School, and then read politics, philosophy and economics at Balliol College, Oxford, where he held the posts of chairman of the Labour Club and, in 1933, president of the Oxford Union.

After university Greenwood continued with political work, which included debating trips to the USA and some freelance journalism.

From 1939 to 1942 Greenwood worked at the Ministry of Information where, in 1941, he became private secretary to the Director-General Walter Monckton, with whom he travelled to Russia and the Middle East.

He led the Labour group on Hampstead Borough Council from 1945 until 1949, and entered Parliament as member for Heywood and Radcliffe in a by-election in February 1946.

Greenwood was the left wing challenger to Hugh Gaitskell in the 1961 leadership election when he received the support of just over a quarter of the Labour MPs.