Henry Swanzy began working for the BBC during the war, reporting for the General Overseas Service. He took over Caribbean Voices after Una Marson, the programme's original architect and first producer, returned to Jamaica in April 1946, and he remained at the helm until 1954. Anne Spry Rush has written of Swanzy having "a great respect for Caribbean writers as representing a legitimate and distinctive element of British literature." Writing in Caribbean Quarterly in 1949, Swanzy commented: "It is not inconceivable that of all the English-speaking world, the West Indies may be revealed as the place most suited for maintenance of a literary tradition." Swanzy is acknowledged to have "transformed Caribbean Voices into the primary site for new and unpublished poetry and prose from the Caribbean, granting an international forum to many who would go on to become the leading lights in Caribbean letters".Writers who received their start on Caribbean Voices or were nurtured as contributors by the programme during Swanzy's tenure include George Lamming, Edgar Mittelholzer, Sam Selvon, Kamau Brathwaite, Austin Clarke, Ian McDonald, John Figueria, Alfred Mended, Derek Walcott and V.S. Naipaul. According to Naipaul, Swanzy brought to the programme "standards and enthusiasm. He took local writing seriously and lifted it above the local."
From 1954 to 1958 Swanzy was seconded as head of programmes to the Gold Coast Broadcasting System (GCBS; later the Ghana Broadcasting Corporation to produce programmes of local content "in the spirit of independence". Swanzy was involved in developing a new weekly literary radio programme called The Singing Net, which encouraged creative writers and attracting contributors and listeners through competitions and articles he wrote for the local press. Swanzy edited an anthology, published the year after Ghana became the first African nation to declare independence from European colonisation, entitled Voices of Ghana: Literary Contributions to the Ghana Broadcasting System 1955-57.