Phillips was born in Gwaun-Cae-Gurwen, Glamorgan, Wales, the daughter of Sally (née Thomas), a teacher, and David Phillips, a steelworker who became a policeman. She began acting professionally at the age of 11 with the Home Service of BBC Radio in Wales. Her first role was as a ginger tom cat. At the same age she won her first speech-and-drama award, for her performance at the National Eisteddfod held at Llandybïe in 1944, where she and a schoolfriend played the parts of two elderly men in a dramatic duologue.
She made her first British television appearance at 17 and won a Welsh acting award at 18. In 1953, while still a student at Cardiff University, she worked as a newsreader and announcer for the BBC in Wales and toured Wales in Welsh-language productions of the Welsh Arts Council.
Phillips was appointed Commander of the Order of the British Empire (CBE) in the 2000 Birthday Honours and Dame Commander of the Order of the British Empire (DBE) in the 2016 New Year Honours for services to drama.