Keeble went to the independent Cheltenham Ladies' College, and later attended St Hugh's College, Oxford, gaining a BA degree in Theology in 1973, and a BA in Sociology from the University of South Africa in 1981. Her father was the British diplomat Sir Curtis Keeble, a former ambassador to East Germany and the USSR. Before entering Parliament she was a journalist in South Africa for the Daily News in Durban from 1973–79 and then in Birmingham on the Birmingham Post from 1978–83. She then worked for the Labour Party as a Press Officer at Labour Headquarters from 1983–84, then the Inner London Education Authority where she was Assistant Director for External Relations from 1984–86, and was Head of Communications for the GMB trade union from 1986–90 before becoming a full-time council leader in inner London. She was a public affairs consultant from 1995–97.
In 1995, Keeble was selected to stand for election for Labour in Northampton North through an all-women shortlist.
Keeble served on the Agriculture Select Committee (before its abolition in 2001), and became Parliamentary Private Secretary to Rt Hon Hilary Armstrong in 1999. After the 2001 general election she was appointed Parliamentary Under Secretary of State at the Department of Transport, Local Government and the Regions, where her responsibilities included planning, regeneration, housing and local transport. She chaired the taskforce on parks and urban green spaces. In 2002 she moved to the Department for International Development. In 2003 she left the frontbench. From 2005, she was a member of the Treasury Select Committee.
Keeble introduced a private members bill to introduce the offence of causing death by careless driving: the measure was later accepted by the Government and introduced in the Road Safety Act 2006. She also introduced ten-minute rule bills on flooding, and a bill on minimum pricing for alcohol.
At the 2010 general election, Keeble lost her seat as MP for Northampton North by 1,937 votes to the Conservative Party candidate Michael Ellis, representing a swing of 6.9%.
Keeble was selected by the Northampton North Constituency Labour Party to fight the seat at the next general election in May 2015. She was once again unsuccessful at the United Kingdom general election, 2015, losing again to Conservative Michael Ellis by 3,245 votes.
Keeble married Andrew Hilary Porter on 9 June 1990 in Camberwell; the couple have a son and daughter. She is an honorary fellow of South Bank University.
Her sister, Jane Mahoney, and her brother-in law Anthony were killed on 12 July 1998 near Darwin in Australia. A Hells Angel motorcyclist had ploughed into them whilst they were waiting by the roadside after Anthony changed a wheel. The Hell's Angel carried on driving and failed to report the accident. After the accident, her father, Sir Curtis Keeble, the former British ambassador to the Soviet Union from 1978–82 and governor of the BBC, had a heart attack.