As a result of Maconchy's successful debut at the ISCM Festival, her music began to feature more prominently both at home and abroad. On 20 January 1936, Pártos Ödön (1907–77) and Salgó Sándor (1909–2007) performed her Prelude, Interlude, and Fugue in Budapest. A mere seven days later, André Mangeot and Beatrice Huckell (1913–98) performed the work at a Lemare concert. This British performance left the critics divided. While the progressive Michel Dimitri Calvocoressi praised Maconchy for her skilful writing in Musical Opinion, the critic in the Observer found the work to be monotonous. Lambert offered his typically misogynist opinion that the work embodied an ‘uncompromising and anti-sensual attitude towards musical texture’. The critic in the Times arrived at a similar conclusion: ‘If she could overcome her dutiful devotion to harshness Miss Maconchy might write something worth having.’ McNaught, on the other hand, showed remarkable restraint, declaring that the instrumental works in the programme simply ‘belonged to the department of modern research, experiment, and labour towards new artistic planes, and could not be sympathetically listened to or reviewed except by one of the same conviction’.

In the late 1930s Maconchy's fraught relationship with the BBC continued, with occasional improvements that were often followed by more setbacks. Though a broadcast of her Quintet for Oboe and Strings was scheduled for 27 January, it was abruptly cancelled on the 24th owing to the recent death of His Majesty George V, who had died four days earlier. Shortly thereafter, the broadcast was rescheduled for 23 March. On 13 February, Maconchy was informed that a broadcast had finally been arranged for her Piano Concerto on 20 March with Harriet Cohen (1895–1967) as soloist and Boult conducting.

A broadcast of another work followed shortly after, with Lemare conducting Great Agrippa, or the Inky Boys on 15 April in a programme that also included Vaughan Williams's Overture to The Wasps, Darnton's Concerto for Viola and String Orchestra, and Jacob's Passacaglia on a well-known theme. While Maconchy was on holiday in Switzerland in April, she received a letter from the BBC, stating that Paul Helsinger, the principal oboist of the Düsseldorf Orchestra, had written to inquire about her quintet.