Former top-cop Andrew Coster's suggested government ministers haven't told the whole truth about their knowledge of the Jevon McSkimming case

Coster's stepped down as head of the Social Investment Agency on Wednesday - after weeks of pressure stemming from a damning IPCA report.

He's claimed he informally briefed former police minister Chris Hipkins and successor Mark Mitchell about the misconduct allegations against his former deputy - something both MPs deny.

Coster told TVNZ's Q & A, he didn't know of Mitchell's office protocol - to redirect McSkimming-related emails away from the Minister.

He says there's no way in the world that staff employed in a minister's office can prevent the minister, or other staff, from seeing email coming in on the minister's email address.

Mitchell says the protocol has been repeatedly verified by several Police employees who were given the instruction by Coster's office.