Twort was educated at South Hampstead High School, the London School of Art, the London Polytechnic and the Slade School of Art.
At the end of World War I she moved to Petersfield, Hampshire where she ran a bookshop at Numbers 1 and 2, The Square. Her studio was above this shop until 1948, when she moved it to the nearby Church Path. Her work was exhibited in the Royal Academy and other galleries.
Twort was a friend of Nevil Shute Norway.
Upon her death, she bequeathed her pictures to Hampshire County Council.