This is TOTALLY my day for recommendations!!
The song you heard was most likely "There Goes the Fear" from the new Doves album, The Last Broadcast, which is absolutely brilliant.
Doves are Andy and Jez Williams and Jimi Goodwin.
They're from northern England (Manchester area).
They used to be a dance/pop band called SubSub who recorded the 1993 club staple "Ain't No Love (Ain't No Use)."
Then their studio burnt to the the ground with all of their equipment and recordings inside.
They rose from the ashes as Doves.
They're touring the US right now with Elbow (who opened for Pete Yorn).
Jimi plays the guitar and the bass upside down.
They are fantastic.
Also, Adam likes them.
Recommended songs that should be easy to find: "The Man Who Told Everything," "Cedar Room," "Break Me Gently," "Words," "Pounding," "There Goes the Fear," and everything else.