"Sunrise" was released as a double A-side along with "The Trees" in October 2001, as a lead-up single before the parent album We Love Life's release in November. It charted in the UK at #23.
Jarvis Cocker has a simple summary of what he was going for in the lyrics: "They say the darkest hour is just before the dawn, don't they? I don't know if it's true, but they say it. I always hate it when you've been at an all-night party and then suddenly the sun starts coming up and you think, 'Why didn't I go home an hour ago?' You feel unnatural because every other creature's just waking up and the birds start doing the dawn chorus and you feel out of step with nature. So on a simple level the song's just about trying to react to the sunrise in a better way and not to screw things up for yourself."
The instrumental to this song bears several noticeable similarities to "Set The Twilight Reeling" by Lou Reed - and given perhaps the similarities in terms of theme (sunset/sunrise/twilight), maybe this link was no coincidence.
The Fat Truckers did a remix of "Sunrise" for the single release - uniquely, they removed all instrumentation and instead composed the track solely from loops and quick-cuts of Jarvis Cocker sighing and breathing heavily. The resulting mix is quite unlike anything you are ever likely to hear.
The BBC satirical comedy show Monkey Dust used "Sunrise" in the soundtrack during it's run from 2003-2005.