Can a private prosecutor start a prosecution for an offence that requires the DPP’s consent?

The CPS Legal Guidance on Private Prosecutions provides as follows:

“If an offence requires the DPP’s consent to prosecute, the private prosecutor must seek that consent. If the proposed prosecution passes the Full Code Test, the CPS will take over the prosecution. Conversely, if the proposed prosecution fails the Test, the DPP’s consent to prosecute will not be given.”