She was born in Birmingham, and with a scholarship, studied English literature at St Hilda's College, Oxford (1950). Her poems were first published when she was at university in the early 1950s. She became a journalist and worked for the Bedfordshire Times, the Oxford Mail and Drum Publications (Johannesburg, South Africa).
Joseph's best known poem, Warning, was written in 1961 and is included in her 1974 collection Rose In the Afternoon and The Oxford Book of Twentieth Century English Verse. Warning was identified as the UK's "most popular post-war poem" in a 1996 poll by the BBC. The second line was the inspiration for the Red Hat Society. Her first book of poems, The Unlooked-for Season won a Gregory Award in 1960 and she won a Cholmondeley Award for her second collection, Rose in the Afternoon in 1974.