Sir Hugh Orde said the officers should follow the lead of their chief constables and apologise for telling the media that the former Conservative chief whip refused to give them a full account of an altercation at the Downing Street gates that became known as the Plebgate incident.
A secret recording of the meeting released by Mitchell suggests that this was not the case. All three men were representatives of the Police Federation, the quasi-union for officers.
Orde said the officers’ standards of conduct had fallen “below that required” of officers.
“The stark facts are the three officers should have apologised in the same manner and style as the chief constables did,” he told the BBC’s Andrew Marr Show.
His intervention comes amid growing concern that Mitchell was the subject of a conspiracy by officers.
The politician was forced to stand down at the end of last year following a month of relentless attacks over an allegation he said the officers manning the Downing Street gates were “plebs”.
Mitchell admitted swearing at officers who refused to open the gates for him but denied he had used the term. CCTV footage has since raised serious questions about the veracity of some of the police accounts and logs leaked to the press.
At the time of incident the Police Federation was battling with the government in a row over pay and conditions.
Eight people, including five officers, have already been arrested in relation to the events and a decision on whether to press charges is expected soon.