I know that school well, I grew up very close to there and my parents still live there (and shop at the Asda 5 min walk from the school!)
I can assure you there will be no 'wealthy' families at the school - based on the national average. It does incredibly well given the area it is in and has great kids from hard working families but it really doesn't feature 'wealth' at all. I do think that they should bring in a uniform coat, rather than ban certain labels and leave the trand to transfer on to something else.
In terms of the real fur thing - aren't the coyotes in plentiful supply/culled so as to avoid being a nuisance? Is there a difference between fur-cruelty and Ugg-boot/Shearling waistcoat cruelty?