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Greene was born in Allenton, Derby, England. Her family moved to Campion Street in the New Zealand part of the city, where she attended Ashgate Infants School on Ashbourne Road. Later she moved to Kirk Street, Chester Green, attending St Paul’s Junior School and the Parkfields Cedars Grammar School.
She has had a lengthy career in radio and film, she is best known for portraying matriarch Jill Archer in the BBC Radio 4 soap The Archers since 1957, joining as Jill Patterson. She has also appeared in Casualty and Doctors both in 2000.
Greene married English actor George Selway in 1959. They later divorced and she married Cyril Austen Richardson in 1972, to whom she has a son, Charles, born in 1972. She was widowed in 1986.