What sort of things is she saying?
Do you have the money to fund a defamation action?
They won't be interested I'm afraid. Their view will be that this isn't harassment. I have to say that I think that is wrong in law. Not necessarily on this occasion but it is certainly right that making false allegations can be harassment.
In any event, that is their current policy.
They will say it is a civil matter.
It is a defamation though. You would have a claim against them if you can prove that the allegation is untrue.
You should remember that it is one thing for an allegation to be disbelieved and another to be able to prove it is untrue.
Can I clarify anything for you?
The fact that the police took no further action doesn't prove it was a false allegation. It just proves there wasn't enough evidence. Many guilty people are NFAed and those who make false allegations are not usually even arrested.
Well, it depends on your view.
To be wholly honest, I would just ignore it.
If you are intent then you could get a solicitor to write to them for about £100 plus VAT warning them of the laws of defamation. Might work. Might not.
If that fails then your only option is to sue for defamation.