I am absolutely flabberghasted that children have to ask permission to remove blazers/sweaters! 
In DD1's school, sweaters underneath blazers are optional (Y to the PP who said that girls never remove them, even in the height of summer...) but blazers may be removed in class as long as they are replaced upon leaving.
In DD2's (super super controlling) school where they are almost obsessive about uniform, the (in their case) all singing, all dancing high-technology fleece (allegedly) jumper again, may be removed in lessons. Without asking.
What concerns me is winter - plain white t-shirts are permitted under blouses, but in DD1's case, there is no room in her locker for a topcoat (she takes gloves at this time of year) and in DD2's school there are no lockers, and due to the all singing, all dancing high-technology nature of the fleece, topcoats are very strongly discouraged.
Showerproof pacamacs which fit into the school bags in cases of exceptional rain are permitted, but DD2 doesn't want. She takes a scarf and gloves in cold weather too, and I've persuaded her to have a very small folding umbrella. Did you see the rain yesterday?
Even high-technology fleeces can't cope.
Basically, neither takes a topcoat - which horrifies my mum! 