Lipman was born in Kingston upon Hull in the East Riding of Yorkshire, England, the daughter of Zelma and Maurice Julius Lipman. Her father was a tailor; he used to have a shop between the Ferens Art Gallery and Monument Bridge.

She attended Newland High School for Girls in Kingston upon Hull and was encouraged into an acting career by her mother, who used to take her to the pantomime and push her onto the stage. Lipman trained at the London Academy of Music and Dramatic Art.

Lipman worked extensively in the theatre following her debut in a stage production of The Knack at the Palace Theatre, Watford and was a member of Laurence Olivier's National Theatre Company at the Old Vic. She made an early film appearance in Up the Junction.

She first gained prominence on television in the 1979 situation comedy Agony, in which she played an agony aunt with a troubled private life. She played the lead role in the television series All at No 20 and took on a range of diverse characters in the series About Face.

She is well-known for playing Joyce Grenfell in the biographical show Re: Joyce!, which she co-wrote with James Roose-Evans, and Beatrice Bellman, a Jewish grandmother in a series of television commercials for British Telecom. She has continued to work in the theatre for over thirty years, playing, amongst other roles, Aunt Eller in the National Theatre's Oklahoma! with Hugh Jackman.

In 2002, she played a snooty landlady, Lillian, in Coronation Street, and a Jewish mother in Roman Polanski's award-winning film The Pianist. More recently, she has narrated two television series on the subject of design, one for UKTV about Art Deco and one about 20th century design for ITV/Sky Travel. In 2003 she appeared in Jonathan Creek in the episode "The Tailor's Dummy".

She also wrote a monthly column for Good Housekeeping magazine for over ten years and recently penned a weekly column in The Guardian in the newspaper's G2 section. She performed as a villain in the 2006 series of Doctor Who in the episode entitled "The Idiot's Lantern" as The Wire. Until April 29, 2006 she played Florence Foster Jenkins in the Olivier Award nominated show Glorious! at the Duchess Theatre in London's West End.

After her playwright husband's death in May 2004 she completed his autobiography By Jack Rosenthal, and played herself in her daughter's four-part adaptation of the book, Jack Rosenthal's Last Act on BBC Radio Four in July 2006. She has created several volumes of autobiography from her Good Housekeeping columns and recently published The Gibbon's In Decline But The Horse Is Stable, a book of animal poems which is illustrated by established cartoonists including Posy Simmonds and Gerald Scarfe, to raise money for the International Myeloma Foundation, to combat the cancer to which she lost her husband.