Charles said he and Queen Camilla were "deeply saddened" at her loss, telling of her "warmth and wit that shone through both on and off the stage".
The double Oscar-winner died in hospital surrounded by family and friends after a seven-decade career that defied the grandmother who once told her she could never go into acting "with a face like that".
Dame Maggie, who was made a DBE in 1990, would say she had wanted to become an actress since childhood, despite never having seen a play or a film until her teens.
She was born in Ilford, Essex, in 1934 but moved to Oxford aged four with pathologist dad Nathaniel and secretary mum Margaret.
She left school at 16 and the following year she starred as Viola in Twelfth Night at the Oxford Playhouse, in 1952.
She was soon spotted by Laurence Olivier, who invited her to join the newly formed Royal National Theatre Company in London.
There, and at the Old Vic, she excelled in both tragedy and comedy, moving easily from Shakespeare to Noel Coward, to Restoration comedy to Ibsen.
She developed her incredible skill among some of Britain's best actors, including Robert Stephens, who was to become her first husband. They married in 1967 and had two sons before divorcing in 1974.
The film industry soon began to recognise her abilities and she was given several supporting roles. Just seven years after her first stage role she had received her first Bafta nomination, for promising newcomer in 1959 for the crime film Nowhere To Go.
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