I also picked this one because the music video is the best, most complete, of the lot. It tells a story but there's a creepy kind of undertone that appeals to the horror movie fan in me. There's an interview with Paloma Faith in which she explains how a lot of the album was inspired by cinema - and you can really see it in this music video.
The song itself is a tragedy. It's about being in love with someone who still in love with someone else. It's the kind of thing you can belt out when you're alone in the house by yourself, hurting a bit and wanting to let it all out. (Don't you feel sorry for my neighbors?)
But this song also makes me giggle a little because when I first listened to it (and for a long time afterward) I thought the lyrics "perfect heart" were actually "perfect whore" - which is also very apropos, given the story of the song.
Fall to Grace is an album that it is absolutely worth buying. Paloma Faith's first album, Do You Want the Truth or Something Beautiful? is good and several of the tracks on it are among my favourites but her second album blows that one out of the water. Buy it. Love it.