His piece `` By the Sleepy Lagoon '' became the signature tune of a radio program called Desert Island Discs . Arthur Wood 's `` Barwick Green '' became the theme of The Archers . Several pieces of light music are used on BBC Radio 4 to the present day , with Eric Coates 's `` By the Sleepy Lagoon '' being the theme of Desert Island Discs , Arthur Wood 's `` Barwick Green '' the theme of The Archers and Ronald Binge 's `` Sailing By '' preceding the late-night shipping forecast .