If it helps, I can narrow down the list to these:
War Cry - Joe Strummer and Richard Norris
Fugue in A-Minor - Brahms
The Killing Moon - Echo & the Bunnymen
A Message to You Rudy - The Specials
Monkey Gone to Heaven - The Pixies
Ace of Spades - Motorhead
In Between Days - The Cure
Your Lucky Day in Hell - The Eels
Sharks Can't Sleep - Tracy Bonham
Little Luxuries - The Burros
You're Wondering Now - The Specials
Big Boss Man - Jimmy Reed
Detroit City - Bobby Bare
White Lines - Grandmaster Melle Mel
Walk Like an Egyptian - The Bangles
Under Pressure - David Bowie (with Queen)
Cities in Dust - Siouxsie & The Banshees
Go - Tones On Tail
The Dominatrix Sleeps Tonight - Dominatrix
Let It Whip - The Dazz Band
Doors of Your Heart - The Beat
Lorca's Novena - The Pogues
I have the OST part 1, and that song's not on it. Plus, I know its definitely not some of the other songs I've deleted from the list (because I've heard them). I'd also say its probably not anything by The Specials (but I'm not an expert in any way). My bet would be on The War Cry, or The Killing Moon. Just a guess though.