Szervánszky studied at the Franz Liszt Academy of Music in Budapest, Hungary with Pál Kadosa and György Kurtág.
In 1979 she took up a position as professor of piano at Musashino Academy of Music in Tokyo and taught in Japan until moving to London in 1986.
She is also in demand for music courses and has taught at the International Bartók Festival in Hungary, the British Kodály Academy, the twentieth-century music course at the Centre Acanthes, Avignon, the Orlando Festival in Holland and the International Musician's Seminar at Prussia Cove.
Since 1979, Szervánszky has concentrated primarily on the piano duo partnership with her husband, Ronald Cavaye and they have performed extensively in Europe and the Far East - particularly in Japan.
Szervánszky and Ronald Cavaye made the first complete CD recording of the first four volumes (solos, duets and two pianos) of Kurtág's collection of pieces Játékok – Games.