Initially a popular singer in the dance band era and a comic actor on the show Much-Binding-in-the-Marsh, he was later a disc jockey for Radio Luxembourg and the BBC.

[1][2] After his crooning days, his BBC radio career began in 1939 with the It's That Man Again (ITMA) shows with Tommy Handley, in which he took the part of Lemuel the office boy.

[2] On Sundays he did both Breakfast Time and Glamorous Nights and he also presented Housewives' Choice and Midday Spin, transitioning to BBC Radio 2 from 1967.

Along with Kenneth Horne, Costa also appeared in an episode of The Men from the Ministry which co-starred Richard Murdoch.

In 1964 he linked a musical short film, Just for You which featured some prominent "pop" bands of the day, including The Applejacks and Freddie and the Dreamers.