In the UK I don't think dress codes mention anything about underwear at all.
The following is fairly typical:
http://www.northlan.gov.uk/education+and+learning/education+services/parental+information/school+dress+code+-+content.html
The idea of 'having to wear a bra' is, unfortunately, due to peer pressure, fear of ridicule, and misplaced sense of modesty/embarrassment
.
If girls/women transferred their behaviour on beaches etc to other appropriate places (the home garden, parks, etc) then there wouldn't be all this paranoia about the 'visible nipple'
PS Regarding the photograph above, you've better eyesight than me if you can see the slightest trace of a nipple bump at all. I agree with fd, I couldn't see the point of posting the photo at all, and it's no big deal whether the girl in question is wearing a bra or not.