York became a star of the stage and screen and was best known for her role in 1969 film They Shoot Horses, Don't They?, for which she won a Bafta and was nominated for the best supporting actress Oscar.
She died at the Royal Marsden Hospital in London on Saturday at the age of 72 after suffering from bone marrow cancer.
Her son, the actor Orlando Wells, said she was admitted to hospital on January 6, three days before her birthday, after suffering pain in her shoulder.
"She was obviously an incredibly brave woman, because she didn't complain at all," he said.
He and sister Sasha are in "terrible shock", but he said of his mother: "From Sasha and my point of view, she was absolutely the centre of our lives. She was a truly, truly wonderful mother."
York enjoyed a varied career that saw her win acclaim for roles in films including A Man For All Seasons, Battle of Britain and Tom Jones.
In more recent years she was seen on television screens in BBC dramas Holby City and Casualty, as well as continuing her work on the stage.
Speaking from his home in south-west London, Wells said: "What always amazed me about mum was how she managed to garner so many strands of her career.
"There was the glamorous Hollywood aspect – she has worked with everyone from John Huston to Sydney Pollack – as well as the big commercial films like Superman.
"On the other hand, she has also worked in theatres above pubs in Islington. She was always prepared to take a risk and to know you can't have a success every time. She was incredibly brave about the artistic choices she made."