They are Agata Zając, Zofia Kiniorska, Aleksandra Melaniuk and Jakub Przybycień.
The other semifinalists are Félix Benati and Nathanaël Iselin of France, Nicolò Foron of Germany, Jiří Habart of the Czech Republic, Nicolas Kierdorf of Luxembourg, and Britain's Matthew Rhodes.
In Wednesday’s semifinals, they will conduct the London Symphony Orchestra in one of three works: Shostakovich’s Cello Concerto No.1, Mozart’s Clarinet Concerto or Sally Beamish’s Variations on a Theme of Benjamin Britten.
Three conductors will be chosen for Thursday’s final round.
Poland's Zając is the Mills Williams Junior Fellow in Conducting at the Royal Northern College of Music in Manchester. She is also continuing her education at the Academy of Music in Kraków, southern Poland.
Meanwhile, Kiniorska is a resident conductor of the Sinfonia Varsovia Orchestra.
Melaniuk is studying conducting at the Academy of Music in Poznań, western Poland.
Przybycień is a master's student and a teaching assistant at the Zurich University of the Arts. He has collaborated with many orchestras in Germany, Switzerland, France, the Czech Republic, Poland and Estonia.
Founded in 1990 by Italian philanthropist Donatella Flick, the London conducting competition is among the most prestigious events of its kind. It is open to conductors who are aged 30 or under and offers them much-needed support at the start of their careers.
Past winners of the Donatella Flick Conducting Competition include Poland’s Michał Dworzyński, who won first prize in 2006.