Thanks for the information
I can see what you are furious about this.
This is very definitely defamation. Some people will tell you that what is said in court is protected and that is all very well but a complaint to the police is not legal proceedings.
The difficulty with defamation actions is that you have to prove that it was false as opposed to just an allegation that was disbelieved. That is hard to do as you will have the burden of proof. However, if you can do that it is worth pursuing.
You could also sue in harassment if there is more than one allegation/incident. I presume this isn’t the first act of vexatious on her part ? There is a fairly settled law now that making false or trivial allegations can be harassment. That does still cost but it is much cheaper.
Or you could get a solicitor to write to her warning him of the laws of harassment and defamation and making clear he should desist. That would only cost about £100 plus VAT.
Given the allegations though, I do think you are right; you need to do something.
Hope this helps. Please let me know if you need more information.