The song that comes to mind is RotherSingaDonSong which is a tribute to the workers of South Yorkshire sung to the tune of the hymn Jesus Christ is Risen Today. As a folk chorus we tend to sing it like a hymn with the concentina sounding a bit like an organ accompaniment.

On the subject of songs for Athiests ( or secular Hummanists if you prefer). I always found it difficult when I stopped believing in God when I was about 11/12. I thought it terribly hypocritical to sing hymns in assemby. Teachers tend not to accept that you are not singing on as a matter of principal. I've got over that and tend to sing to appreciate a good tune. I also sing a weddings etc because you are then doing it for your friends. I suppose any songs that about generally looking after your fellow man are hummanist songs. What about some of Burns - A Man's a Man for all that.

All the best

Julie