As a child, she survived the Second World War first in a sheltered house on Pozsonyi Street, Budapest, and then in the ghetto (November 1944 – January 1945).[3]
From 1956 to 1961, Elek studied at the University of Theatre and Film Arts in Budapest, in the class of film director Félix Máriássy. Her classmates included Pál Gábor, Imre Gyöngyössy, Zoltán Huszárik, Ferenc Kardos, Zsolt Kézdi-Kovács, János Rózsa, Éva Singer and István Szabó.[4]
During this time she was a founding member of the Balázs Béla Studio, a workshop for experimental film. In 1968, Elek made her first feature film, Sziget a szárazföldön (The Lady from Constantinople). From the 1980s onwards, she made historical films such as The Trial of Martinovics and the Hungarian Jacobins (1980). In the 1990s, she shot films with a Jewish theme like Tutajosok (Memories of a River, 1990) and To speak the Unspeakable: The Message of Elie Wiesel (1996).
Elek was married to the Hungarian film director Zsolt Kézdi-Kovács (1936–2014). The cinematographer and producer Eli Laszlo Berger Eli Berger (László Berger, born in Budapest, 1970) is their son, known for the films A hét nyolcadik napja (The Eighth Day of the Week, 2006, directed by Judit Elek), Bankster (2016) and Dreams Are an Excuse (2023).[5]