Not a James Blunt fan, but I am a HUGE fan of Ben Folds, and I'd second the recommendation for Joe Jackson, and add Elvis Costello to the mix. Both these guys have a "pop but so much more" aesthetic to them - kind of the art-house weirdos that managed to write some pretty damn appealing music, much like Folds, IMO. You might even like Billy Bragg, but I think that could be pushing it.
Both Jackson and Costello have extensive "greatest hits" catalogues, though as ever, if you are so inclined, the LPs should be the goal.
You may also like Ben Lee (a little more folky), but I'm not too sure. Not a huge fan myself.
And Elliot Smith wrote some absolutely amazing music, highly worth checking into. My first experience with him came from his album XO, prompted by what I heard from the Good Will Hunting Soundtrack.
Ooh! And the Apples in Stereo! Man, I guess I could go on and on...
Oh, and this is something completely different, but do yourself a favour and pick up "Coast to Coast Motel" or "Philadelphonic" by G. Love & Special Sauce. The former is the pinnacle of the band's raw, bluesy sound, while the latter is their best work with a smooth, slick sound.