OP exactly the same thing happened to me, with them victimising a 5 year old like this and then blaming me. It's disgusting that school staff and Local Authority staff can repeatedly break the law, deny a child safe access to education, and yet it is down to the parent to have to try and enforce the law and - if they do - many school staff behave like this, gaslighting and lying about the parent. After our Head teacher's third malicious referral SS visited my house for 10 minutes, declared it was clearly a waste of their time and told the Head not to make baseless referrals and waste their time again.
The resemblance of this Head's behaviour to the one you describe is uncanny. Perhaps this playbook is what they study for CPD on INSET days? 3.5 months my 5 year old was unable to attend safely before the Head or SENCO would even have a phone call to discuss the situation. Disgraceful and so unprofessional.
In any normal profession the regulator and professional body would take legal action when such egregious and illegal behaviour is reported to them. Staff involved should be suspended pending investigation then struck off and personally fined as well as large fines being levied on the organisation. It's the only thing these types of people would understand. The education system is toxic.
Many individual class-level teachers are competent and try hard but sadly it seems the worst bullies and victims of Dunning-Kruger get promoted to management even though they are completely incompetent. And then sadly there is also a subset of more junior staff who are either naive or not very bright or suffering from ostrich syndrome (I guess it helps them sleep at night) who purportedly believe all teachers can do no wrong and join in slinging mud at any parent who tries to get the school to comply with the most basic legal requirements.
Sadly nothing will change until there is an overhaul of the whole system and these people are struck off and prevented from working in education, as they should be for deliberately breaking the law and continuing to do so even when it is explicitly brought to their attention.
Sadly, other posters are right that you'll only get anywhere with an EHCP and they will obstruct it at every stage. The entire system is a joke and to treat the most vulnerable children and their parents in such a callous manner is beyond vile. I hope you and your DD are as ok as you can be in the circumstances. It is absolutely not your fault, it is a clear pattern of behaviour as can be seen from the posts on this thread: school staff who think they know better than doctors and specialists even though it's clear they know less about autism than you'd learn in a half hour training course, it is quite astonishing, the sheer arrogance of it. They wreck children's lives with their behaviour but they do not care. But I expect SS will have seen this over and over again and if a Head is behaving like this you are very unlikely to be the first family they have done this to so SS will already know their reputation. They will have to follow up on the referral but will likely put the Head in her place as they did with ours so try not to worry.