Cooper was born in Liverpool, the daughter of deaf parents. She was educated at St Oswald's Roman Catholic Primary School and Bellerive Convent Grammar School in Dingle, Liverpool. She then attended the University of Liverpool.
Cooper originally worked for a company called W. Cooper Ltd from 1973 to 1980, before joining Littlewoods initially as a buyer when, in 1994, she became the public relations manager and then, in 1995, the group corporate communications manager. She became a project coordinator in 1999, before she left Littlewoods in 2001, when she was appointed director at the Merseyside Centre for the Deaf.
She was a member of the Liverpool Health Authority and held the position of vice chair between 1994 and 1996. In 1996, she became Chair of Liverpool Women's Hospital.
She has also acted as a trustee of the Roy Castle Lung Cancer Foundation.
Cooper was elected, aged 22, to the Liverpool City Council as a Liberal councillor in 1973 and, in 1992, became the Lord Mayor of Liverpool; she stood down from the city council in 2000.
She fought her first Westminster campaign at the 1983 General Election when she was selected to contest the Conservative-held seat of Liverpool Garston where she finished in third place, with more than 14,000 votes behind the winner Eddie Loyden.
Next, Cooper contested the 1986 Knowsley North by-election, caused by the resignation of the Labour MP Robert Kilroy-Silk to become a television presenter. At the by-election Labour retained the seat with George Howarth gaining a comfortable margin of 6,724 votes, and she did not do much better when she contested the seat again a few months later at the 1987 General Election, finishing 21,098 votes behind Howarth.
At the 1992 General Election, now a Liberal Democrat, she was back in her native Liverpool, coming second at Liverpool Broadgreen 7,027 votes behind Labour's Jane Kennedy, but ahead of the former deselected Labour MP Terry Fields.
From 1973 to 1984, Cooper was councillor for the Broadgreen ward. From 1986 to 2000, Cooper represented the Aigburth ward, before in 1999 she switched to the Labour Party, and stood in Netherly ward in 2000. She contested the European Parliament elections in 2004 in for Labour in the North West.
Coopper became the Labour Party's candidate from an all-female short list, in the constituency of West Lancashire at the 2005 General Election, following the retirement of the sitting MP Colin Pickthall. Cooper was first elected to the House of Commons at her fifth attempt with a majority of 6,084. She made her maiden speech on 24 May 2005.
Since 2005, she has been a member of the Northern Ireland Affairs Committee, and was part of the successful campaign that stopped the merger of the Southport and Ormskirk hospitals. In June 2006 she became Parliamentary Private Secretary to Rt Hon Lord Rooker, a Minister at the Department for Environment, Food and Rural Affairs.
On 9 August 2006, The Daily Telegraph wrote that Cooper had written to the Prime Minister's office reporting the viewpoint of some of her constituents expressed to her, that they would be appalled, if Margaret Thatcher, Baroness Thatcher of Kesteven were given a state funeral, as a leader more politically divisive than others of the late twentieth century.
In 2007, she became Parliamentary Private Secretary to Ben Bradshaw, initially when he was Minister of State in the Department of Health until 2009, when she remained his PPS when he was made Secretary of State for Culture, Media and Sport. She is a member of the All-Party Parliamentary Health Select Committee.
In August 2013, she became one of the few Labour MPs to vote against the Marriage (Same Sex Couples) Bill, which eventually passed with cross party support.