Godson is the younger of the two sons of Joseph ("Joe") Godson (1913-1986), a Polish-born Jewish-American diplomat who gained a law degree at New York University in 1940, and had been a Marxist in his early years later joining the Lovestoneites (adherents of Jay Lovestone Joe subsequently served as labor attaché at the American Embassy in Ottawa (to 1952) and in London (1953-9), of Hugh Gaitskell, leader of the Labour Party 1955-63, whom he assisted in his battle against the left-wing tendency of the party. Joe was also a friend of the prominent Labour Party and trade union figures Harold Wilson, George Brown, Arthur Deakin and Frank Chapple. In 1976, during his retirement spent in London, Joe established the Labour Committee for Transatlantic Understanding, funded by NATO, now the Trade Union Committee for European and Transatlantic Understanding (TUCETU), a "direct expression of American influence within the wider British labour movement" Godson was suspected by many in the UK Labour movement to be a CIA operative, and "although there were rumours in London during the 1950s that a CIA officer was operating under cover as a Labour attaché, Hugh Wilford concludes there is no evidence that Godson was a CIA officer". Stephen Dorril and Robin Ramsay refer to Joe as "an American spook" in their biography of Harold Wilson.