An independent review has been ordered by the body representing rank-and-file police officers into “issues” raised by its handling of the “Plebgate” row.
Police Federation chairman Paul McKeever has acknowledged concerns that it "stoked up" the Downing Street incident which led to Andrew Mitchell quitting the Cabinet.
He said this week that he would apologise to the MP if it was shown he had been wrongly accused of calling officers "plebs" in a bust-up over their refusal to let him ride his bike through the gates.
Mr McKeever has handed control to his successor-elect Steve Williams just over a month before he is officially due to leave the role, due to "pre-existing leave arrangements", the Federation said.
And one of Mr Williams' first acts was to announce plans for the review.
"Recent events have shown that there are issues around the way the Police Federation nationally is able to lead and co-ordinate at a national, regional and local level," he said in a statement.
As we enter a new era, my first act as chairman is to establish this independent panel to ensure that we as the Federation continue to represent the interests of our members in the most effective and efficient way."
Local branches organised protests by members wearing "PC Pleb" T-shirts and some demanded Mr Mitchell's sacking.
Scotland Yard is now investigating the possibility that the ex-Cabinet minister was the victim of a conspiracy and have made two arrests - one of them a member of the diplomatic protection squad.
That officer is said to have emailed his local MP, Tory deputy chief whip John Randall, posing as a member of the public and accusing Mr Mitchell of calling police "plebs".
Mr McKeever conceded on Thursday: "I think we can all say we could have done things better."
He said it was right to await the results of the police investigation, which involves around 30 officers and is being supervised by the Independent Police Complaints Commission (IPCC).
But he said if it showed Mr Mitchell had been wrongly accused he would be "one of the first in the queue to apologise".
Also on Thursday, police arrested and questioned a 23-year-old man, who is not a police officer or member of police staff, on suspicion of intentionally encouraging or assisting the commission of an indictable offence on December 14.
That date was a day before a member of the diplomatic protection group was arrested on suspicion of misconduct in public office related to the email to Mr Randall purporting to be from a passer-by who witnessed the event.
It came as the president of the Association of Chief Police Officers, Sir Hugh Orde, played down the prospect of a serious rift between the police and politicians over the episode.
"I don't think this is prima facie evidence of a growing distrust. There is an individual case and we need to look at that and it is being looked at," he told BBC Radio 4.
"But the only facts around that case that are clear is that there was an interaction and the chief whip did choose to apologise for his behaviour.
"The great strength of the service is that if things are found wanting they will be dealt with transparently and openly and the public will be made aware of them."
He said it was proper, in a more general sense, for there to be "a healthy tension between politicians and the police".
Mr Mitchell admits swearing in the exchanges with the officer on the scene - to whom he apologised after the incident - but has strenuously denied calling him or colleagues "plebs".