Below are songs that have the same (or nearly the same) titles as popular Church songs, but are, in fact, completely different. I list these so others don't make the mistake of tracking them down in hopes of hearing a Church cover. If you can provide info on any more, please contact me.

Performer Album Song Title Notes
B.B.C. n/a Under The Milkyway Tonight B.B.C. is a German hate crust group, and this song is on the similarly titled, 4-track 7" 45 released on Bastard Records in 1993. Rather than being an interesting cover of a beautiful song, this is just a noisy diatribe against America.
The Durbervilles Alternative Route To All Destinations Unguarded Moment This song by a British folk/country group (with a show on BBC Radio Leeds) is about a dog chained up outside that hears a sound.
Steve Forde Steve Forde Metropolis Despite Steve being from New South Wales, this slow, almost stereotypical country song is not a Church cover.
Mark Fry Shooting The Moon Under The Milky Way This is the opening track on what is only the second album by this enigmatic English artist. Fry first gained notoriety with his 1972 psych-folk debut album, the cult classic "Dreaming With Alice". And although this song is not a Church cover, it's gentle beauty perfectly complements the Church song.
Pop Crash Colapso Searching Some Recreation Under The Milky Way A raucous and crude song by this Spanish punk band from 1992.
Sojo Glider Vibrating & Amplified Comedown Sojo Glider is a French band that lists The Church as one of their influences. But despite having Dare Mason as producer on this, their sophomore album of 2005, the track Comedown has nothing in common with the high-powered, pure-pop Church track from "Magician Among The Spirits."
Tweeter 07 AM EP & Skinny EP Under The Milky Way This song by the accomplished DJ and producer from Santiago, Chile is not the church song, but a nearly 8-minute techno/house journey into echo and reverb with a funky backbeat.
Van Classica Under The Milkyway Van is a Swedish project which specialized in Euro House/dance covers of classical music. They only released this one album, as well as the singles "Winter in Paradise" and "Ice Got My Love."
deejay mystik (dj mystik) Oracle: Episode One Under The Milky Way This is a bootleg of the Van version, illegally compiled with other neo-disco crap of other artists by dj mystik and sold/distributed mainly through the online asian trance scene.