Part of the official guidance on this is that it is good practise to have a protocol agreed between parents, school and school nurse. We did this when dd was first diagnosed and it was helpful. We all knew exactly what was meant to happen. Part of the protocol was that the parent would be telephoned after each reaction, as soon as the medical treatment had been dealt with. Another part was that an ambulance must be called for each reaction. The nurse sent me a suggested protocol so that was standard across the whole LEA area. If they'd called out an ambulance twice in one week you can bet the NHS would put pressure on them to manage nuts better.
Fortunately that school was good about banning nuts and my child isn't as sensitive as yours, so I never had to test it worked. If she'd had a reaction I would have expected to go in then and there - or at least at the next break time - to make sure she was OK if she hadn't been taken to hospital. I know its more difficult for you with a baby but if the reaction's lunch time and she's still at school in the afternoon she's going to be harder to comfort.
Sadly I know now that not all authorities are so strict, but our new LEA still has a protocol and it still includes contacting parents. I can't remember what it said about ambulances, I'll check. If you think a copy of our protocol(s) would help put pressure on your LEA/nurse send me your address and I'll post it/them.
Your problem is more with the parents than the head/governors. The school could be more pro-active by saying that any child found with peanut in their lunch will have it removed and not have any lunch. Or they could set aside an area in which nuts could be eaten and supervise it so that any child there had to wash thoroughly afterwards. They can write to the parents of the children concerned explaining exactly what has happened. There isn't a lot else they can do.
I would get the kids round to your house, show them a video and get them to practise with an out of date epipen.