I would pull them up and say that they're not safeguarding the children if they're making them wear a thick wool blazer in this sort of heat - especially if they're in a school that gets hotter indoors during the day in the summer... If they splutter and say that it's not safeguarding then ask what they would call it because it's certainly not looking after the best interests of the pupils or the teachers. I would also ask to see their risk assessment for having pupils in school in their wool blazers on days when the outside temperature is 24C, 28C, 32C and higher, what provisions are made to check the temperature inside (guessing different rooms will have different temperatures depending on windows, ventilation, shade, kit (cookery room or computer room likely to be hotter than a history room for example), doing PE, and at what point do they allow the pupils to take off their uniform, given that the World Health Organisation suggests that 24C is the maximum for comfortable indoor working and anything above 26C as unacceptable - and that would be assuming that 'appropriate' clothing would be worn too...
Any chances that there's a parent that's a doctor or HSE official that could pull them up on this and point out it's dangerous?
I was at a private school in the 80s where they were crazy about uniform - but in the summer there was no way they would make us wear jumpers or blazers, you got to choose yourself when you were in shirt sleeves or wore a jumper or a summer uniform dress. I remember once in 5 years being told we had to wear a blazer to look smart - it wasn't a particularly hot summer's day, but it was founders day so one of those strange ones when the whole school was on display and they liked everyone to look the same. But that was for an hour or two, not all day, and on a special occasion. Other years if it was hot they would make everybody wear the summer dress uniform without a blazer so we all looked the same for the occasion. They didn't want kids keeling over! Much more sensible approach.
Unfortunately there's no maximum temperature specified for working in an office in the UK, the regulations just say that it needs to be reasonable (there's a minimum set of 16C though!). I don't know how they can argue that this heat is reasonable - particularly if they make the kids wear a thick jacket.
Just out of interest - are all the staff wearing thick jackets too?
It might be worth contacting the HSE to see if there is anything they could say that would help to sway the minds of the school...
These articles are interesting:
bbc
document
mumsnet with interesting link