Though Maconchy's relationship with the BBC remained strained throughout 1951, the organisation did at least remain true to its word in regards to her Concertino for Piano and String Orchestra, which was included in a Third Programme broadcast on 21 February 1951. The work, which is cast in three movements, was played by the Kathleen Merritt Orchestra conducted by Merritt, with Margaret Kitchin (1914–2008) as the featured soloist. The broadcast elicited an encouraging letter from Vaughan Williams, who wrote to Maconchy on 28 February: ‘Your work came as a great relief. It had vitality and purpose. I won't say more after just a first hearing without seeing the score. You are getting performed at last, I am so glad.’ Another performance of the work took place later in the year on 2 October at the Wigmore Hall featuring the London Chamber Orchestra conducted by Anthony Bernard, with Kathleen Cooper as soloist. This latter performance earned highly favourable notices in the press, with the critic in the Times lauding the slow movement for ‘its smouldering romanticism’.

In the spring, Maconchy's String Quartet No. 6, which she had completed the previous year, was premièred by the Martin String Quartet at an LCMC concert held at the RBA Galleries on 22 May. This concert was part of the London Season of the Arts, coinciding with the Festival of Britain, commemorating the centenary of the Royal Exhibition. True to Maconchy's musical idiom, each movement is constructed around a series of motifs expressed at the outset. As the first few measures of the first movement, Passacaglia, illustrate, ascending leaps, followed by two consecutive falling thirds and its inversional equivalent, play a pivotal role, serving as the basis for melodic and harmonic development (Example 8.1). As the movement progresses, Maconchy varies the primary theme and motifs contained within it by means of rhythmic variation and melodic expansion and contraction. The primary theme, however, never loses its dominance, and remains a persistent driving force throughout.

In the vivacious second movement, Allegro scherzando, the opening material in the first violin yields all the clues to the motific material used in the movement, such as its opening flourish and descending octave leaps.