Hmm, I don't know about this, Toffy! I've only heard "I don't have an accent" coming from Americans, which is strange, because I also hear Americans talk about other Americans' accents (Southern, Bostonian, New Yorker, etc.)

I lived in England for 8 years and I can't recall any English person saying they don't have an accent. Of course, English accents vary substantially between regions (and class, but that's another story) so it might seem very strange to claim that one doesn't have an accent.