It is essential to remember that the standards applicable to those conducting a private prosecution are of the highest order. That starts with the requirement that an application for a summons must disclose all of the information that is material to the decision of the Court, which includes of course any material adverse to the application or which might militate against it.
The nature and extent of the duties upon private prosecutors, at all stages of the process, are set out in the PPA’s Code for Private Prosecutors, which can be found here: https://private-prosecutions.com/wp-content/uploads/PPA-Code-for-Private-Prosecutors.pdf