Her son Orlando Wells confirmed that she passed away on Friday after a long battle against cancer.
Susannah first found fame in the 1960s, enjoying a successful career in film, on TV and on the stage.
She was nominated for an Oscar for her role in the 1969 film They Shoot Horses, Don’t They? and won a Bafta for the same role.
Her other notable films included The Killing Of Sister George and A Man For All Seasons, while she also starred in two Superman films, in 1978 and 1980, as the superhero’s mother Lara.
More recently she joined the cast of Holby City in 2003 in a recurring role as hospital manager Helen Grant. She also played the character on two episodes of Casualty.
She married Michael Wells in 1960, with whom she had two children, Orlando and her daughter Sasha. The couple divorce in 1976 and Susannah never remarried. She is also survived by a grandson, Rafferty, and a granddaughter.
Her son told the Telegraph she was an “absolutely fantastic mother”.
“She loved nothing more than cooking a good Sunday roast and sitting around a fire of a winter’s evening,” he said.
“In some sense, she was quite a home girl. Both Sasha and I feel incredibly lucky to have her as a mother.”