I also prefer my bras unpadded. And often find myself buying bras only to cut off surplus ribbons etc as soon as I get them home. If you are happy with lacy but otherwise unembellished, my current favourite is the Gossard Reverie range (available padded and unpadded) which you can still buy from various discount retailers on eBay. Infuriatingly the current Gossard range does seem entirely padded.

Unpadded cotton bras do seem astonishingly hard to find. BHS make some dull but functional ones. I've tried the Figleaves basics but they were poorly made and the underwires stabbed me. Calvin Klein occasionally make nice, long-lasting unpadded cotton bras, but more often they are too "structured" for my paste.

Oxford is rubbish for buying lingerie in person :( I loathe Bravissimo and anyway I'm too small for most of their range.