Unless your child never attends residentials or socialises outside of school, your child is going to experience brand snobbery in a uniform school.
DD at uniformed school was desperately worried about her clothes for a school residental. I flatly refused to buy brands, partly cost, partly on principle.
She saved her own pocket money to upgrade the supermarket trainers I could afford to a much loved pair of nikes
She got some Nike tshirts for her birthday.
I then picked up a couple of branded sweatshirts second hand as good as new, because frankly they were decent quality.
It's worth pointing out at this point the clothes she wore for her residential formed the bulk of her home wardrobe for many years after. If she didn't need school uniform she would have happily worn them to school as well. The Nike trainers lasted 6 years.
At that point i started to reexamine what i knew about label snobbery. DD and I then started looking at thing like did the clothes offer good value for money, were they comfortable, were they decent fabric. DD started to become adept at spotting fakes.
DS hollister tracksuit bottoms cost only a couple of pounds more than primark.
DD's secondary school (deprived area) the kids all wore kickers boots or DM boots because they lasted (Not unusual for them to be passed sibling to sibling).
Nike and branded clothing was being handed sibling to sibling regardless of gender or being sold on second hand. Branded clothing was being picked up cheap at a nearby outlet and being sold on after use.
Brand snobbery at DD's deprived area school was as much about what people could afford as what they couldn't.