By their very nature, these are very personal, creative ceremonies, so the music possibilities are endless. Non-religious or religious music are both suitable for a Civil Funeral, though Humanist services are purely non-religious.
Your choice of music
Civil funeral services have very little formal structure so you can have as much or as little music as you wish. Having a solo song or two during a service gives another 'voice' apart from your celebrant. (They are often the only person speaking, as many families find reading a tribute too emotional for them.)
Top songs for civil funerals