Kids are not stupid, they don't bully you in front of teachers but they are like sharks smelling blood in the water and know days like this makes those with less money a prime target for their viciousness.
This is a weird way of describing teenagers.
Again, I still don't think (unless you're attending a strangely materialistic school) that it would end up about money, honestly. You could get a gorgeous outfit from Primark for less than ten or fifteen pounds.
If you have a bullying culture then you shouldn't be slapping flimsy plasters on, you should be treating the wound. Allowing kids to just be nasty in different, more inventive ways does not make the bullying less impactful, it just makes it easier to slip under the radar. The school is confident that they're taking measures to prevent bullying, while doing nothing.
Kids with poor fashion sense are probably going to be battered on that anyway, poor things, it's not like banning Own Clothes Days means that other children won't know what their own clothes look like! Especially in the days of social media.
It won't stop bullying, or bullies. Even with uniform the bits you have more leeway with (skirt cut, socks/tights, shoes, bags) will give the kids an idea of who has more fashion sense. If you're wearing a second-hand uniform or don't get a new blazer every year they'll notice that too.
I can see the benefits of uniform but I hate hate hate the notion that it will somehow prevent bullying.