Born in Leeds and educated at the University of Oxford (Queen's College), he became a Fabian Society staffer and a political journalist on the Daily Mirror and the New Statesman. He was a member of Prime Minister Harold Wilson's informal "kitchen cabinet". In 1965 he became a Labour Party press officer. He was elected MP for Ardwick in Manchester in 1970 and has represented Manchester Gorton since 1983.
He was a minister throughout Labour's time in power in the 1970s, first in the Department of the Environment, then in the Department of Industry. In opposition he became Shadow Home Secretary and Shadow Foreign Secretary. In 1992 he went to the back benches and became Chair of what was then the National Heritage committee.
He is the writer of several books, of which the best known is How to be a Minister (1980), an irreverent look at the difficulties faced by ministers trying to control the civil service, in much the same vein as the television series Yes, Minister. He also wrote scripts for the 1960s television satire That Was The Week That Was.
Kaufman is an outspoken opponent of hunting with hounds. He is also one of Britain's most prominent Jewish critics of Israel.