At age 16 Natasha won a scholarship to the Royal College of Music and studied with Clifford Curzon and Arthur Benjamin. After the Second World War, she gave a concert at the former Bergen-Belsen concentration camp to inmates who were recovering in its hospital wing. She was the soloist in the world's first televised concert for the BBC.
In her forties she was forced to give up the piano because of breast cancer, which affected her arm muscles, but she quickly re-established herself as an academic specialising in the psychology of music, and contributed to the Grove Dictionary of Music and Musicians.
She first met Stephen Spender in 1940, marrying him in 1941, and the couple were for many years part of a literary circle which included W. H. Auden, Christopher Isherwood, T. S. Eliot and Sir Isaiah Berlin. Their daughter Lizzie is married to the Australian actor/comedian Barry Humphries, and their son Matthew Spender is married to the daughter of the Armenian-born artist Arshile Gorky.
A collection of writings, about her late husband and her passion for gardening, An English Garden in Provence, appeared in 2004.