In general, BBC Radio 4 is a speech-only radio station. It very rarely plays pieces of music in their entirety.
There are some music-focused programmes on BBC Radio 4 such as Desert Island Discs. However, in this programme, only short excerpts of music are used.
Another programme in which you will hear music is Sunday Worship. This programme broadcasts a church service, which usually includes choral music.
BBC Radio 4 also broadcasts documentaries about music, which naturally feature excerpts of music. One interesting documentary series is Soul Music, in which each episode explores the personal effects of a piece of music on several individuals’ lives.
BBC Radio 4 has always been news and speech-based rather than music-focused. The station was created in 1967 to replace the Home Service, which was the BBC’s news, drama and discussion station (in contrast to the music-focused Light Programme, which became BBC Radio 2).
BBC Radio 2 and Radio 4 remain the UK’s most popular radio stations.