His area of study was primarily history of Poland, history of the United States and history of the interwar period. Zaremba was an editor of Orzeł Biały ("The White Eagle") and Pokrzywy ("Nettles"), managing director of publishing house Gryf in London, collaborator with the Parisian Kultura ("The Culture"). In 1967 he became a collaborator with Polish section of the Radio Free Europe.
He was an observer during the Spanish Civil War (1936–1939) and participant of the Invasion of Poland (1939).
Until the end of World World War II Zaremba stayed in the Oflag VII-A Murnau Prisoner Of War camp in Murnau am Staffelsee. After liberation, Zaremba joined to II Corps in Italy.
In 1946 he settled in England.