Here's another band that you have to check out: Baby's Gang. This is sort of an 80's group of small girls (I assume) that sing disco songs with a pronounced Italian accent. I have to say that I think that there is something to singing songs in English with a real accent, such as Björk does.
Now I just have to find that record. I heard about this through Dagensskiva.se, a Swedish podcast that showcases interesting new (and old) music. Look for the episode with "Jamin" in it.