Una Marson was born and grew up in Jamaica. After her work on the editorial staff of the Jamaica Critic in 1926, she founded her own magazine The Cosmopolitan, which she also edited. Having established herself in Jamaica, Marson moved to London in 1932 to experience life outside Jamaica and to find a wider audience for her literary work. She lodged with Harold Arundel Moody, and became involved with the League of Coloured Peoples. She worked for the League as its unpaid Assistant Secretary, organising student activities, receptions, meetings, trips and concerts. During her stay in England from Marson continued to publish on feminist issues, as she had in Jamaica. She also became increasingly interested in discussions about race, eugenics and the colour-bar, focussing on the most pressing issues faced by black migrants living in Britain.

During her first stay in Britain, Marson organized, staged and compered an evening of entertainment at the Indian Students Hostel. The line-up included the American singer John Payne, the pianist Bruce Wendell and the Guyanese clarinettist Rudolph Dunbar. By 1937 she was editor of the League’s journal and its spokesperson, working closely with Moody. Marson was also a member of the International Alliance of Women for Equal Suffrage and Citizenship and the British Commonwealth League (BCL). At the latter she met Myra Steadman, daughter of the suffragette Myra Sadd Brown. The All India Women’s congress was affiliated with the BCL. During the period she also became involved with the Left Book Club and encountered the writings of Rabindranath Tagore.

After two years in Jamaica, Marson returned to Britain in 1938. In 1939 Marson was offered work by the BBC as a freelancer for the magazine programme 'Picture Page' to arrange interviews with visitors from the Empire. She also drafted three-minute scripts for the programme. After the outbreak of the Second World War, Marson lectured occasionally at the Imperial Institute and worked as a talks and script writer for the BBC. In 1941 she was appointed full-time programme assistant to the BBC Empire Service, where she hosted and coordinated the broadcasts under the title 'Calling the West Indies'.

In November 1942 George Orwell asked her to contribute to the six-part poetry magazine 'Voice', broadcast on the Indian Section of the BBC’s Eastern Service, with Marson taking part in the fourth programme dedicated to American poetry, which also featured William Empson. She read her poem ‘Banjo Boy’. In the December edition of the programme she appeared alongside M. J. Tambimuttu, T. S. Eliot, Mulk Raj Anand, Narayana Menon and William Empson. This led Una to devise a similar programme for the West Indies, titled 'Caribbean Voices', which in later years under the direction of Henry Swanzy would introduce authors such as George Lamming, Sam Selvon, V. S. Naipaul and Edward Kamau Braithwaite to a wider audience. The programme ran for fifteen years until 1958. She returned to Jamaica in 1945 and died in 1965 from a heart attack.