Redman was born in Brighton. Her father, Ronald Jack Redman (1929–1980), was born in Camberwell, London to parents from the East End, and her mother, Joan Beryl Redman (née Herrington, 1927–2014), was born in India as the daughter of William Herrington, a British Indian Army soldier. Redman’s father, who was two years younger than her mother, died at the age of 51 in 1980, when Redman was 23. Redman had one brother, who died in 2008

In 1984 she appeared as Marina in the BBC Shakespeare production of Pericles, Prince of Tyre opposite Mike Gwilym. She also played Maxine in Oxbridge Blues, a British television mini-series, produced by the BBC and first shown in 1984 written by Frederick Raphael. In 1985 she played Janet in the touring version of The Rocky Horror Show.

Redman married actor Robert Glenister in 1984; the couple had one child together, daughter Emily, before they divorced in 1992. She is credited with having encouraged her then-brother-in-law, Philip Glenister, who played DCI Gene Hunt in Life on Mars and Ashes to Ashes, to go to drama school and to pursue acting.

In 1986 she played Miss Fairfax (Gwendolen) in the BBC Drama production of The Importance Of Being Earnest by Oscar Wilde.

She played opposite Liv Ullmann in Richard’s Things (1980), took over from Alfred Molina in the 1990s comedy drama El C.I.D., playing a new female lead in the series, and played Diana Dors in the TV film The Blonde Bombshell (1999). She presented an MTV show on satellite TV in the 1990s. She co-starred in the first two series of Dangerfield in 1995, playing Joanna Stevens, and played a role in Taggart the same year. In 2000 she played Deedee Dove in the feature film Sexy Beast. From 2000 until 2003 she played Alison Braithwaite, a woman whose life is turned upside down after she wins the lottery, in ITV’s At Home with the Braithwaites. Beginning in 2003, Redman took the role of DSI Sandra Pullman in the BBC’s New Tricks.

In June 2006 Redman performed in Children’s Party at the Palace as Cruella DeVil for the Queen’s 80th birthday, and was the subject of an episode of the BBC documentary series Who Do You Think You Are?, a programme that explored her family history.

Redman was appointed a Member of the Order of the British Empire (MBE) in the 2012 Birthday Honours for services to drama and charity.

In July 2013, she announced that she would be leaving New Tricks; Tamzin Outhwaite replaced her. In 2015, she played the role of Jackie Rose in the three-part ITV drama The Trials of Jimmy Rose, starring alongside Ray Winstone. From 2017, she played Lydia Fonseca in the ITV drama series The Good Karma Hospital.

In 2018, she became a patron of Brighton Open Air Theatre. She told the Brighton Argus: