She grew up in East Sussex, the daughter of Lord and Lady Longford, and sister of Antonia Fraser.
She took a Modern History degree and on 22 February 1998, married lawyer and writer Irving Weinman; Harry Mathews wrote an Epithalamium for Judith Kazantzis and Irving Weinman. They have two children.
She worked for the Chelsea Labour Party, and reviewed for the Evening Standard. During the 1970s she turned to poetry, fiction, painting and printmaking. She lived in London, and spent three months a year in Key West. Around 2000, she returned to live in Lewes, in East Sussex.
In the 1990s she worked for Kalayaan - Justice for Migrant Domestic Workers. In 1999 she left Tony Blair’s Labour Party, and since 2001 helped to campaign for Occupied Palestine. In 2003, she signed the Statement for Peace of the 21st Key West Literary Seminar.
In August 2010 Kazantzis contributed to an eBook collection of political poems entitled Emergency Verse - Poetry in Defence of the Welfare State edited by Alan Morrison
Her poems have appeared in London Magazine, Stand, Ambit, Agenda, Poetry Review, Poetry London, Poetry Wales, Bete Noire, The Honest Ulsterman, Poetry Ireland, Red Pepper, The Independent, The New Statesman, Tribune, and Banipal.