In September 1948, pianist Harriet Cohen, Bax's former love and a champion of his works, severely injured her right wrist. Bax's response was to compose a piano concerto for the left hand only, just as Maurice Ravel had done for pianist Paul Wittgenstein 20 years earlier. Evidently, Bax had a hard time with the Concertante for Piano, for he wrote to a friend, "I find it terribly difficult to think of anything effective for the one hand. But then I am very much out of practice in writing for the piano at all."
Bax dedicated the Concertante for Piano to Harriet Cohen, who gave its first performance on July 4, 1950, at the Cheltenham Festival with the Hallé Orchestra under John Barbirolli. Three weeks later Cohen performed the work in London at the Royal Albert Hall with the BBC Symphony Orchestra under Malcolm Sargent. Chappell published a transcription of the slow movement for solo piano in 1950; otherwise, the piece has not been printed. Despite the work's poor reception at its premiere (auditors found it old-fashioned and too intimate) Harriet played the Concertante regularly for several years.
Bax employs his typical forces. Supporting the piano are three flutes with piccolo, two oboes with English horn, two clarinets, two bassoons, four horns, three trumpets, three trombones, tuba, timpani, harp, percussion, and strings.
Tragedy informs the plaintive first movement of the Concertante. In a letter to a friend, Bax wrote that he was inspired to compose the first movement by John Brophy's Sarah, a book about the perils of Robert Emmet and Sarah Curran in 1803. In sonata form, the movement features a secondary theme that returns in an unexpected place near the end, but is layered with an earlier violin part. Much of the writing for piano is linear and with two lines, resulting in many held notes in either the thumb or little finger. However, the range is narrow enough for Cohen's small hand.
Bax's second movement is the most successful of the Concertante's three movements. Warmth pervades the ternary construction, the lovely melodies of which prompted Chappell's reduction for solo piano.
The Finale is a rondo that opens with percussion in a manner similar to the "Adam's Fates" section of Arthur Bliss' Adam Zero, a work popular at the time Bax was at work on the Concertante for Piano. The main theme is uninspired and has led at least one critic to proclaim the Concertante "Bax's worst extended work."
The Concertante for Piano and Orchestra was among the last of his own works Bax heard. Along with The Garden of Fand and the Overture to Adventure, it was performed, by Cohen with the Radio Eireann Symphony Orchestra under Aloys Fleischmann in Dublin on September 29, 1953, with the composer in attendance. Four days later, Bax died.