This, IMO, is a stupid, unnecessary rule. However, I may be biased as my DD had a very unpleasant meeting with a teacher at the beginning of the day.
She was twelve at the time and had just walked two miles to school on a hot September day (but winter uniform, so long sleeves and ti.) Blazer was in her arm as it's black and hot and heavy!
She got shouted out at in front of friends and students, "HOW DARE YOU WALK TO SCHOOL WITHOUT YOUR BLAZER." Supposed to be representing the school, etc... [hmm
She came home and told me. We reviewed school rules and there was NOTHIG about this supposed rule of wearing full uniform.
Other children also had issues... were shouted at for wearing waterproof boots home/to school when it was snowing or raining! Kids on bikes told to ride wearing blazer instead it being in bag when they are quite long and could get caught!
Eventually some of us parents wrote a letter to school and they said it was okay, finally accepted that a) sometimes children don't want to wear the uniform outside of school, if the school day has ended, they should be allowed to just enjoy themselves and be kids b) it's impractical and even dangerous sometimes, ie, in heat or bikes, and c) uniform wasn't going to create a good impression with all the children crossing the road like idiots and the older ones swearing!