She was best known for her roles in Coronation Street, Tenko and Doc Martin.
Her agent John Grant said she had been living with Alzheimer’s disease for some years.
In a statement on behalf of her family, he said: “It is with great sadness that we announce the passing of Stephanie Cole, OBE.
“She passed away this morning at the age of 84. Stephanie had been living with Alzheimer’s disease for some years.
“Stephanie was an extraordinary talent whose long and distinguished career included many iconic performances in theatre and television.
“She brought joy to millions through her many much-loved roles in sitcom and drama. She will also be remembered for her tireless work supporting mental health charities.
“During this incredibly difficult time, the family kindly requests privacy.”
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