For clarity (and not having a go at you at all), there are two sets of guidance.
There is non-statutory guidance issued last month. That is indeed just guidance and schools are free to ignore it. All that says about branded items is that schools should "consider how any branded items if they choose to have them, are sourced".
The statutory guidance, issued in 2021, says that, before summer 2022, schools should make changes to their uniform policy such as removing unnecessary branded items. However, it also says that branded items should be kept to a minimum and used only for low cost or long-lasting items.
I obviously don't know what uniform policy your school has adopted, but you need to be sure that, if challenged through judicial review, you can show that you have indeed kept branded items to a minimum and used them only for low cost or long-lasting items. If you haven't, you would need to show that there are exceptional circumstances that allow you to depart from the statutory guidance.
Remember that the courts will not accept that a branded item is necessary just because the governors think it is and have minuted their reasons. And this is the fundamental problem. I'm not saying it is the case at your school, but I see far too many schools that insist things like specific, non-generic designs of jumpers, sweatshirts, cardigans, socks, etc. are necessary. It is, in my view, unlikely that the courts would agree.