Graham was educated at the
Co-operative College and held several positions in the
co-operative movement from 1939, becoming National Secretary for the
Co-operative Party. He was a councillor on
Enfield Borough Council from 1961, joining the new
London Borough of Enfield in 1964 and is a former leader of the London Borough of Enfield. In 1966, Graham contested
Enfield West at
that year's general election. He was Labour
Chief Whip 1990–97. He was chairman of the Co-operative Council, and served as
President of the 1987
Co-operative Congress. Graham was President of the Institute of Meat and Patron of the
Ancient Order of Foresters and of the Edmonton
Constituency Labour Party. On 18 December 1986, Graham was the only Peer in the House of Lords to speak against Lord Halsbury's Local Government Act 1986 (Amendment) Bill, which sought to prohibit the "promotion of homosexuality" by local authorities. ==Personal life==