Korda was born in Singapore, into a creative family of entertainers, professional singers, songwriters, and accomplished musicians. His father, Hungarian-born Tibor Kunstler, was a violinist and former student of the Franz Liszt Conservatory of Music in Budapest, Hungary and Academia La Scala in Milan. Tibor played saxophone on Coleman Hawkins' tour of the East. Korda's British mother, Shirley Green—who worked under the stage name Shirley Lenner—was a vocalist and actress. She starred in "Those Kids From Town" (1942) and also sang with Joe Loss, George Elrick, and Stéphane Grappelli.