In a statement, her agent Lionel Larner said: “’Glenda Jackson, two-time Academy Award-winning actress and politician, died peacefully at her home in Blackheath, London this morning after a brief illness with her family at her side.
“She recently completed filming ‘The Great Escaper’ in which she co-starred with Michael Caine.”
Jackson won the Oscar for Best Actress twice for Women In Love in 1970 and A Touch Of Class in 1973 as part of the so-called acting ‘Triple Crown’ - she also won three Emmy Awards and a Tony Award across her distinguished career.
In the midst of her showbiz career Jackson took a hiatus from acting to focus on politics.
In 1992 she was elected as the Labour MP for Hampstead and Highgate and served as a junior transport minister from 1997 to 1999 during Sir Tony Blair’s government.
Sir Keir Starmer said: “I was very sad to hear of Glenda Jackson’s passing. She leaves a space in our cultural and political life that can never be filled.
“She played many roles with great distinction, passion and commitment.
“From award-winning actor to campaigner and activist to Labour MP and government minister, Glenda Jackson was always fighting for human rights and social justice.
“As a fellow north London MP, I know how much she was loved and respected by her constituents.”
The Labour leader also evoked her famous appearance on Morecambe and Wise as Cleopatra, with a play on her line, “All men are fools, and what makes them so is having beauty like what I have got”.
He said: “Of course no tribute to Glenda could fail to mention her role as Cleopatra in that most famous and loved of all the Morecambe and Wise sketches.
“We will never see talent like what she has got again.”
Diane Abbott, who became a Labour MP in 1987, five years before Jackson was elected, has said she was ” kind and extremely principled”.
Tagging Jackson’s son, Mail on Sunday columnist Dan Hodges, Ms Abbott tweeted: “Very sad to hear of the death of Glenda Jackson.
“I served alongside her in Parliament for many years. She was a kind and extremely principled woman.”
Former Downing Street communications chief Alastair Campbell has said Jackson “found the transition to politics harder than she expected” but had “a great life well lived”.
Mr Campbell, who worked with Labour prime minister Sir Tony Blair, under whom Jackson was a minister for transport from 1997 to 1999, tweeted: “Sad to hear that Glenda Jackson has died.
“One of the finest actresses of our lifetime, our local MP and for a time minister in (Tony Blair) government.
“I sometimes felt she found the transition to politics harder than she expected. But a great life well lived and a major contribution on so many fronts.”
Labour MP Tulip Siddiq tweeted: “Devastated to hear that my predecessor Glenda Jackson has died. A formidable politician, an amazing actress and a very supportive mentor to me. Hampstead and Kilburn will miss you Glenda.”
Rishi Sunak’s thoughts are with Jackson’s friends and family, Downing Street said.
The Prime Minister’s spokesman said: “Obviously that’s extremely sad news and obviously his thoughts will be with her friends and family at this time, but I’m sure we will have more to say.”
Jackson stood down as an MP at the 2015 general election and returned to acting, both on the stage and in front of the camera.
She won a Bafta for best actress in 2019 for her role in Elizabeth Is Missing, which followed the story of a woman suffering from dementia.
Paying tribute, Labour MP Karl Turner tweeted: “I am so very sorry to hear this news. When I was elected in 2010 my office was opposite Glenda in 1 Parliament Street. Glenda was always very supportive to me and provided great advice on occasion. True socialist.”
Jackson had just finishing filming The Great Escaper alongside fellow double Oscar-winner Sir Michael Caine, who she had last acted with 48 years ago in The Romantic Englishwoman.
Their new film tells a story, inspired by true events, of a Second World War veteran who escaped his care home in Hove, East Sussex, to attend a commemoration of the 70th anniversary of the D-Day landings in France.
Jackson said she only started acting after she failed her school certificate, leaving her with no option but to start working at the age of 16.After joining a friend at the YMCA amateur dramatics society while she was working at her local Boots store, she went on to study at Royal Academy of Dramatic Art (Rada).
She also played Egyptian queen Cleopatra in 1971 for an episode of The Morecambe & Wise Show with comedy duo Eric Morecambe and Ernie Wise.