In a criminal trial it is for the prosecution to prove, beyond reasonable doubt, that the offence was committed. This is a hefty burden. It is not for the defence to prove anything to any standard at all, and certainly not beyond reasonable doubt.
All the defence has to do is to cast sufficient doubt in the minds of the jury or magistrates to ensure they are not sure and certain and they must acquit. So it is unlikely that evidence would be produced to show, beyond reasonable doubt, that the offence was not committed. It is simply not the job of the defence to do so. Further, if such evidence did exist it would almost certainly be in the possession of the CPS and they would not continue the prosecution.
I accept the question is hypothetical, so hypothetically the basis to sue the police or the CPS is unlikely to exist.