Her younger brother was Colonel Pilot Kazimierz Leski, codename "Bradl", an intelligence officer in the Polish Home Army.

In September 1939, she was called up for auxiliary military service, appointed a wartime Podporuchik (second lieutenant) and assigned to the Staff Squadron of the Air Command Eskadry Sztabowej Dowództwa Lotnictwa.

Pilots were instructed to move the planes out of the forest between air raids, and take off rapidly without waiting for the engine to warm up.

[4] She made her way to the United Kingdom via Romania and France, where she began her efforts to become a member of the British Air Transport Auxiliary (ATA).

From early 1941 she piloted aircraft from factories and repair shops to field airfields, and took part in flying equipment transfers.

[15] In 2005, Anna Leska, Stefania Wojtulanis-Karpińska and Jadwiga Piłsudska featured in Polki Nad Londynem, a documentary about their wartime flying experiences.

[17][18] A caricature of Leska as Pilot First Officer, with her signature on it is held in the Archiwum Akt Nowych archives in Poland[19] and she was one of the Mothers of Polish Independence featured in the Matki Niepodległości Polski exhibition there in 2022.