Something for the USians to chew on: as far as I can tell, the linked article is about a UK 'comprehensive' school, not a private school.
It will therefore be state-funded (centrally, not locally), and will cater to children from a wide range of income-brackets, from 'upper-middle class parents who can afford expensive holidays abroad twice a year (but can't quite afford to send little Tiffany to private school)' to 'council-estate parents who've been on unemployment-benefit ever since they left school themselves'. Uniforms will likely be compulsory (when I was at secondary school, 'non-uniform days' happened once a year, if that), which itself is not cheap these days (especially when it all has to be replaced after every growth spurt -- or bought 2 sizes too large to start with). Most comprehensive schools in Britain no longer require kids to wear a school blazer as part of the uniform -- because those things really are expensive.
So (apart from the fit of their 'uniforms') one of the major differentiators between the richer and poorer kids will be (the visible cost of) their non-standard accessories: jackets, rucksacks, pencil-cases, phones, whatever. So yeah, the (nastier) rich kids will very likely be giving the poorer kids grief for not having expensive-label jackets, because (nasty rich) kids will always act like (nasty rich) kids, regardless of which continent they're on.
Not agreeing that banning expensive stuff from the school is necessarily the best way of dealing with this, though...