As a family, we’re great fans of BBC 1’s “Death in Paradise”. We particularly like the theme tune. A little research showed that the tune is an instrumental version of a classic reggae song. “You’re wondering now” is the song. It was written by Reuben “Andy” Anderson (according to the label of the original release on C&N records). The “Death in Paradise” theme rendition was composed by Magnus Fiennes.
The original version appears to be by Andy and Joey in 1964. The YouTube clip below shows a 1966 recording of some joyous dancing to the song.
Some websites say the original version was by the Skatalites, but on their official discography I can only find later versions on compilation albums. Their version is below also, together with the Series 3 opening titles from “Death in Paradise”.