Wallfisch was born in London on June 15, 1953. His mother was a cellist and his father a pianist. Young Raphael, after studies on the violin and piano, turned to the cello at age eight. His list of teachers is impressive: at home he studied with Amaryllis Fleming (1967-1969) and Derek Simpson (at the Royal Academy of Music from 1970-1973), and abroad with Amadeo Baldovino (Italy; 1969) and Gregor Piatigorsky (the U.S.).
It was through his studies with Piatigorsky in California that he was given the opportunity to perform in several private recitals with Jascha Heifetz. Wallfisch won first prize in Florence, Italy, at the Gaspar Cassadò International Cello Competition in 1977. Thereafter, his career grew in several directions: as a soloist he regularly appeared in recitals and with British orchestras; in 1980 he began a 12-year stint playing in a duo with his father, Peter, while serving as a professor of music at the Guildhall School of Music and Drama in London. He would later teach cello at the Zürich Winterthur Konservatorium and Hochschule in Mainz, Germany.
In the 1980s Wallfisch gained an international reputation from his appearances throughout Europe and the U.S. In 1982 he started a long relationship with the English label Chandos: among his earliest recordings were a coupling of the Barber Cello Concerto and the Shostakovich First Cello Concerto (1982) and a disc of Tchaikovsky works that included the original version of the Rococo Variations (1983). Over the next decade or so he would make more than 20 recordings for Chandos. Since the 1990s he has branched out his recording activity to include other labels. Among later recordings is his two-disc set of the complete works for cello by Shostakovich on Nimbus (2006). Shostakovich was also featured, along with J.S. Bach and Tchaikovsky, in his successful concert tours of the U.K. and Germany in the fall of 2006. Further efforts included recordings of Zemlinsky's Cello Sonata (2007) and the cello sonatas of Chopin, Laks, and Szymanowski (2010).