Although Everywhere At the End of Time by The Caretaker is depressing, the music undeniably slaps sometimes. So here are some of the songs I could find as someone who listens to a lot of 1930s music
The songs highlighted in green are the ones I know
A1. It's Just A Burning Memory
A2. We Don't Have Many Days
Say It Isn't So by Rudy Vallée
A3. Late Afternoon Drifting
Not actually sure of this one but the chords sound a bit like Dancing in the Moonlight by Rudy Vallée
A4. Childishly Fresh Eyes
Moonlight and Shadows by Russ Morgan and his orchestra
A6. Things That Are Beautiful and Transient
B1. All That Follows is True
It Looks Like Rain in Cherry Blossom Lane by Carroll Gibbons
B3.Quiet Internal Rebellions
B4. The Loves of My Entire Life
B5. Into Each Other's Eyes
B6. My Heart Will Stop in Joy
Room With A View by Russ Morgan and his orchestra
Lullaby of the Leaves by Henry Hall
C3. What Does it Matter How My Heart Breaks
I think it's just a swung version of Heartaches by Al Bowlly
Goodnight, My Beautiful by Russ Morgan and his orchestra
Heartaches by Al Bowlly, near the end of the song, after Al has stopped singing
E4. Libet's All Joyful Camaraderie
Goodnight, My Beautiful by Russ Morgan and his orchestra
F2. Drifting Time Misplaced
Lullaby of the Leaves - Henry Hall
Goodnight, My Beautiful by Russ Morgan and his orchestra
At this point the music is either indecipherable white noise or various different songs jumbled together
Some of these are songs that are impossible to find but some of them are just ones I don't know. So I will keep looking!!!