Definitely Big Audio Dynamite (BAD)
Also:
The Stranglers
Wall of Vodoo
Big Country
Fine Young Cannibals
Erasure - two guys basically...
Enigma
I forgot Lowen & Navarro; incredible musicians!
Your Wall of Voodoo mention reminded me that Stan Ridgeway has put out some great solo albums. He is underrated as a solo artist.
Another one: Robbie Williams.