Joanna Drew was born in India to Brigadier Francis Greville Drew and his wife and artist, Sannie Drew. She was educated at Dartington Hall and then at Edinburgh University and Edinburgh College of Art, studying both Art and Art History. She worked for the Arts Council for nearly four decades as an exhibition organiser. Among the most iconic shows she oversaw at Tate were Fernando Gamboa's 1953 exhibition of Mexican Art, the legendary 1960 Picasso exhibition, the 1964 Miró exhibition and the 1968 exhibition of Henry Moore to celebrate the artist's 70th Birthday. She was a great supporter of the Arnolfini in Bristol, the Oxford Museum of Modern Art, and the Whitechapel Gallery in London, among other institutions, becoming Director of The Hayward Gallery from 1987 until her retirement in 1992.

Joanna was described in her obituary in The Telegraph as "unquestionably the most important individual in the British art scene" (22 April 2003). Peter de Francia was her most meaningful relationship and life-long friend, and the present portrait would have been painted when the couple were in France, in 1951. Joanna, like Peter, was bilingual in French, and established important and lasting links with the Grand Palais in Paris, aided by her membership of the Réunion des Musées National. Apart from being honoured with a CBE in 1985, she also received many French honours.