Brophy, the daughter of an archibishop, attended St Paul's Girls' School, London, before going to St Hugh's College, Oxford, in 1947. She was sent down after two years for "unspecified offences", variously rumored to be drunkness in chapel, or lesbianism.

In 1954 she married Michael levey, an art historian. Their unconventional marriage, as well as Brophy's outspoken views in favour of bisexuality and against monogamy, drew the public attention to them. John Bailey, husband of the novelist Iris Murdoch, reports that Brophy tried to seduce Murdoch.

In her later years Brophy suffered from multiple sclerosis.