Well speaking as someone who has been an insurance broker to several NHS Trusts, let alone local councils/LEA's - insurers will want to know in what circumstances the school will need to 'do whatever it is they need to do'. They won't actually need any childs name or address. So I think the school are being a bit OTT frankly - Yes they need to say 'we have a child that has T1 diabetes and we need to administer his lunchtime jab, test his blood, see to it that we have and can administer hypo remedy of choice' or whatever it is they need to do for the child. And also what training they've had to do all this. But that's all. And I wouldn't expect them to ask parent's permission, if you don't identify the child, why would they need permission? - you already give them parental-type responsibility when you leave the child inside their door.
What do they do with asthmatic children? - or children with broken bones in plaster etc?
I mean if something awful happened and they needed to use CPR, someone might sue them or something - but really the only difference is, this one is every day not once in a blue moon.
So I'd just ask em what details they plan on releasing! And if you aren't happy with the answer, ring the LEA to find out why.