Powell was best known for playing headmistress Bridget McClusky between 1981 and 1991 and also appeared in Channel 4 comedy show Man Down.
Her representative Matthew Lacey said in a statement on behalf of the family that the actress died “after complications following a major operation for a perforated colon”.
She died last Thursday in Brighton and the statement added: “She passed away peacefully, with her husband (Alan Leith) and niece at her bedside.
“Gwyneth will be greatly missed by her adoring family and friends along with her many fans from multiple TV appearances.”
Patricia Hidalgo, director of BBC Children’s and Education: “We are very sorry to hear of the passing of Gwyneth Powell.
“Her famous portrayal of Mrs McClusky is one that will be fondly remembered by all those that grew up watching Grange Hill.
“Our thoughts are with her family and friends at this sad time.”
Powell was born in Manchester on July 5 1946 and landed her first major television role in the 1971 London Weekend Television dystopian drama series The Guardians.
Although she secured regular work and appeared in a series of TV dramas, her career accelerated after being cast in the children’s series Grange Hill, about life in a comprehensive school.
She played the tough but fair headmistress Bridget McClusky for a decade until requesting she was written out so she could pursue other roles.
Her other credits included Heartbeat, Holby City and Father Brown, and in 2013 she was cast as the mother of Welsh comic Greg Davies’ character in Channel 4 comedy Man Down.
Powell was married to fellow actor Alan Leith.