It was first performed in Boston on 25 January 1957, by Piatigorsky with the Boston Symphony Orchestra under Charles Munch. It received its first British performance three weeks later, on 13 February 1957, again with Piatigorsky, this time with the BBC Symphony Orchestra under Sir Malcolm Sargent. It received its first recording shortly after this, with the original forces.
The concerto is in three movements: Moderato, Allegro appassionato and finally Theme and improvisations.
The finale contains four improvisations, two each for orchestra alone and solo cello, and ends Adagio, quietly. Piatigorsky told Walton that the violinist Jascha Heifetz had some reservations about the ending, so the composer provided an alternative ending, but ultimately his first version was the version that was premiered. In 1975 Piatigorsky himself asked Walton to revise the ending. He did so, but Piatigorsky's illness (and death) prevented him from performing that version, and it remains unheard.
The concerto has been described as subdued, brittle, lyrical, bittersweet, ruminative and introspective.
Walton regarded the Cello Concerto more favourably than his Violin or Viola concertos.
Walton's regular arranger, Roy Douglas, made an arrangement for cello and piano.
Cellists who have recorded the concerto since Piatigorsky include Pierre Fournier, Paul Tortelier, János Starker, Ralph Kirshbaum, Yo-Yo Ma, Raphael Wallfisch, Lynn Harrell, Pieter Wispelwey, Julian Lloyd Webber, Paul Watkins and others.
Laura van der Heijden won the 2012 BBC Young Musician Competition playing this concerto.