Sir Bernard Hogan-Howe, the Metropolitan Police Commissioner, said it was â€œtoo muchâ€ for police officers or their Federation representatives to call for members of the Government to resign.
He added that officers investigating whether there was â€œany evidence of a conspiracyâ€ against Mr Mitchel,l expect any potential charges to be brought by the end of the month.
Mr Mitchell stepped down in October after being accused of calling police on duty in Downing Street â€œ****ing plebs”.
Sir Bernardâ€™s comments come after Mr Mitchell claimed his career was destroyed by certain elements of the police who had launched a â€œsmear campaign” against him in pursuit of their own political agenda.
Local Federation branches organised protests by members wearing “PC Pleb” T-shirts and demanded Mr Mitchell’s sacking.
Rank-and-file officers were wrong to call for the resignation of the then-Chief Whip Andrew Mitchell over the plebgate row, Britain’s most senior officer has said.
Ken Mackaill, chairman of the West Mercia Police Federation, also said the minister’s insistence that he did not use the word “pleb” meant he was effectively accusing officers of lying, and that he had “no option” but to resign.
The Federation, which represents rank-and-file officers, has since said it planned an independent review into “issues” with its operations.
Sir Bernard told MPs: â€œMy concern would be, from some of the public statements of the Federation representatives, was that they seemed to explicitly get involved in asking for the resignation of a Government member.
â€œFor me, I think that is too much. I think thatâ€™s a decision for a Government to make, or a Prime Minister to make, and I donâ€™t think itâ€™s for police officers to get involved in.
â€œI think itâ€™s not for the Police Federation or for police officers generally to call for the resignation of members of the Government.â€
Mr Mitchellâ€™s claims that politically-motivated police officers conspired to “smear” him and “toxify” the Government came after it emerged that a member of Downing Streetâ€™s Diplomatic Protection Group had written an email to one of Mr Mitchellâ€™s colleagues, purporting to be from a member of the public and alleging that he had witnessed the spat.
The email, which was sent to the deputy chief whip, John Randall, also appeared to corroborate the allegations that Mr Mitchell had used the phrase â€œ****ing plebs”.
But that officer, 52-year-old Keith Willis, a father of three from Ruislip, North West London, has since been arrested on suspicion of committing misconduct in public office.
The police file on the investigation could be handed to the Crown Prosecution Service (CPS) by the end of the month, Sir Bernard told MPs on the Commons home affairs select committee.
“We expect we may be able to share a report with the CPS by the end of this month. A matter of weeks before we do as much as we can,” he said.
The Metropolitan Police Commissioner also insisted he had an â€œopen mindâ€ over the investigation, telling MPs that if any of his previous comments supporting his officers had led others to doubt that then â€œIâ€™m sorry about thatâ€.
He also said officers were right to tell Mr Mitchell he had to use the side gate to Downing Street with his bike, as the main gate should only be opened for vehicles for security reasons.
Mr Mitchell has admitted swearing as officers refused to let him ride his bike through the vehicle gates during the incident on September 19, but has always denied using the world plebs.
CCTV footage of the incident appeared to undermine statements made by officers in the official police log of the incident, which was later published in The Daily Telegraph.
The log included a comment that members of the public witnessed the row and appeared “visibly shocked” when in fact only a few people walked past the gates at the relevant time, appearing to pay no attention to what was going on.
From the Telegraph