Born in Buenos Aires to a Scottish father and American mother, Agar moved with her family to London in 1911. After attending Heathfield St Mary's School, she studied, beginning in 1919, at the Byam Shaw School of Art. Then, in 1924, she studied under Leon Underwood at his school at Brook Green. She attended the Slade School of Fine Art in London from 1925 to 1926. She also studied art in Paris from 1928 to 1930.