Oh gosh.
I've just read the whole thread. Firstly, well done. Secondly, they are now seemingly trying to intimidate you and other parents.
It's perfectly legitimate for you to have a free and frank sharing of views with other parents and sharing the emails with those parents was necessary for the free and frank sharing of views on how to proceed/tackle the situation, they cannot police your or others private correspondence or ask you to delete as you haven't defamed the school (taking it here that you were factual in your communications and have not said anything that is false), you merely brought a matter to their attention (parents) which is in the interests of all parents, you took those legitimate concerns to the school, concerns that needed attention and which they then attended to - reinforcing that those concerns were legitimate.
Download the parent policy as a PP has already mentioned so that you have the current copy. I would also be tempted to ask them, in writing, for any copy of said policy that you have signed.
Any policy that the school may have in place is nothing more than a plan drafted by them/governing body/academy trust/LA (depending on the 'type' of school) to help guide it in managing or dealing with a particular matter.
It is neither prescriptive, nor enforceable and certainly does not supersede legislation. A parent - home agreement is not enforceable btw.
Perhaps ask them for their complaints procedure. It will be on the website (as required by law to be), but it may be an idea to actually ask for it. But that's just what I would do.
You did them a favour and this is how they respond? You could have gone above their heads about it, but you didn't.
You've stayed very calm. If it was me, I would be checking every single policy that they MUST have (must as in legal requirement) and checking that they complied with legislation, including their determined admission arrangements. But that's me, because I don't take kindly to threats.
Whatever you do, when you respond, you need to include what transpired in the phone call - you will need a paper trail.
And, not just now, but when the time is right, submit a Subject Access Request.
Defamation (alledged defamation) is not a police matter. I might just ask them to also detail the reasons for their allegations. You can't respond properly to an allegation of defamation (or anything else) without the reasons for the allegation clearly spelt out along with their EVIDENCE for such an accusation. Again, paper trail.
I'm cross on your behalf. Stay strong. Bullying is not acceptable.