Rae Jenkins was born Henry Horatio Jenkins on 19 April 1903 at 13 Hall Street, Ammanford, Carmarthenshire, the son of Henry Jenkins, a colliery labourer, and his wife Ann, who were also caretakers of the town's Ebenezer Baptist Church. Given a violin by his grandfather at the age of four, he was taught by George Evans, a local collier and talented fiddler, who also found him work playing in the small band that accompanied silent films at the Ammanford cinema. His nickname "Rae" evolved from a two-stage contraction of Horatio, via "Ratio".
After a brief spell working at the Betws and Tir-y-Dial collieries, Jenkins won a place at the Royal Academy of Music before his eighteenth birthday, studying violin under Hans Wessley, viola under Lionel Tertis, and conducting under Sir Henry Wood, who went on to engage him as a violinist in his Queen's Hall Orchestra. By the outbreak of the Second World War, Jenkins was an established figure in both classical and light music circles in London, forming "The Caravan Players" to broadcast gypsy music for the BBC, a lifelong interest that saw him amass a collection of more than two thousand pieces. He became conductor of the BBC Midland Light Orchestra in 1942 and the BBC Variety Orchestra in 1946.
Jenkins became a household name after the war as music director for Tommy Handley's hugely popular radio show "It's That Man Again" (ITMA), where the catchphrase exchange "Play Rae" and "Right you are Tommy bach" delighted listeners nationwide. In 1950 he was appointed conductor of the BBC Welsh Orchestra, a post he held for fifteen years until 1965, playing an important part in the orchestra's post-war development. He was appointed MBE for services to music in 1966 and had previously been made a Fellow of the Royal Academy of Music. A plaque in his memory was unveiled at Ammanford Town Hall following his death.