Okay, fine. 
The guitar lines definitely sound post-punk to me. You hear Blur and Jam in Art Brut? Interesting. I’m not sure how you get either, as both Blur and Jam are very melodic bands, and I don’t think of Art Brut as being particularly melodic with its shouted/spoken lyrics. The only song on that disc that perhaps reminds me of either band is “Emily Kane.”
I’m not completely crazy, as a search for “Art Brut” and “Gang of Four” will reveal a number of reviewers who hear the similarity. Sure, Art Brut isn’t as Gang of Four-y as Bloc Party, but the guitar lines (need I use the overused “angular” to describe them) are definitely reminiscent of that sort of post-punk–at least to my ears. I’m having a much harder time hearing Britpop and mod influences in Art Brut than post-punk.
Yeah, I think you’re right that my view is probably the minority. Maybe I place a higher priority on lyrics and imagery-- when I listen to Bang Bang Rock & Roll, I get the same mental images and feelings that I get from listening to Face to Face (the archetypal Britpop album IMO), not Silent Alarm. Does that make any sense?
FWIW, I do think of Art Brut as a melodic band, though I agree that the guitar line from, say, “Bad Weekend” does have the angularity of a postpunk song.
The truth is that Art Brut straddles at least post-punk and Buzzcock’s era/style punk. They obviously draw from many influences, and post-punk is only a small part of it. “Emily Kane” definitely has a sort of Kinks-iness to it but, overall, sonically I hear them closer to late-70s,early-80s punk/post-punk/New Wave than 90s Britpop which was quite different.
When I say “melodic band,” I mean, can you whistle the main melody that the singer is singing? I can’t whistle “We Formed a Band,” “My Brother,” or even “Emily Kane.” I can’t get to my Art Brut at the moment, but off the top of my head, I can’t think of a single strong melody on that album. Not a strike against them, as I think they’re the most fun (along with the Futureheads) of the latest crop of British acts that I’ve heard, but they’re not melodic in the sense that I’m talking about.
Do the vocals have to be the source of the memorable melody though? I agree that “Formed a Band” isn’t really melodic in any sense, but I can certainly whistle the tune of the others-- I’m just whistling the guitar or bass part.
For what I consider Britpop, I would say yes. We’re just using different definitions of melodic. I should have clarified that I mean “melodic vocals” when I say a song is melodic.
Interesting. I’m not sure how much I agree with that; food for thought.
Thanks for an engaging round of music geekery. 
The more I think about it, the more I realize that while most of the bands I’m thinking of do have strong vocal melodies (Oasis, Suede, Blur), it’s the presence of strong hooks that make Britpop what it is. Usually, the hooks are vocal melodies, but I can think of a few (like Blur’s Song 2) where it’s not melody carrying the hook.