Annesley enrolled at the Royal Academy of Dramatic Art in 1913 after attending finishing school in Dresden and studying French in Paris. While there she met Miles Malleson, whom she married on 12 April 1915 at the age of 19. The couple divorced in December 1922 after Miles failed to comply with a decree for restitution of conjugal rights obtained by Constance on 15 May the same year. After graduating she and spent the 1922 season with the Plymouth Repertory Theatre as lead actress. Malleson took up acting because she believed "that every woman ought to be able to earn a living." She was concerned with fair wages for all actors going on to speak publicly about the importance of securing the minimum wage of 3 pounds a week and payment for rehearsal for everyone, not just lead actors.