Commissioner Sir Mark Rowley says the public should "prepare for more painful stories" as the force confronts the issues it faces.
He said cases included "violence against women and girls offences", such as domestic abuse and sex offences.
"There's a trickle of them and more are going to be surfacing," he added.
Sir Mark was speaking to the London Assembly's Police and Crime Committee in the wake of the case of PC David Carrick, who admitted dozens of rape and sexual offences against 12 women on 16 January.
Carrick was finally stopped when one woman decided to report him following publicity about disgraced Met officer PC Wayne Couzens, who abducted, raped and murdered Sarah Everard.
The Met chief also mentioned the case of PC Hussain Chehab, who pleaded guilty to child sex offences on Tuesday.
The force is currently in a form of special measures, following a series of damning reviews and scandals.
Sir Mark urged the public not to lose heart as the Met rooted out hundreds of corrupt officers thought to be serving.
He told the committee: "We haven't applied the same sense of ruthlessness to guarding our own integrity that we routinely apply to confronting criminals - and I'm deeply sorry for that."
He also said: "Lifting the stone and revealing painful truths will not be resolved overnight, and I mustn't pretend it will do, and I hope you understand that that can't be done.
"We have to prepare for more painful stories as we confront the issues that we face."
During the meeting, he also revealed a new Met corruption hotline had received tens of calls each week, a third of which related to other forces, which had been passed on.
But he stressed progress with wider reforms of the Met "won't be rapid".
Responding to questions by the committee about whether certain Met teams have more abusive or corrupt officers, Sir Mark said they were looking at units for "warning signs". Carrick served in the same policing unit as Couzens.
"This is pockets, but it's too many pockets that exist because systematically we haven't been good enough," he added.
He emphasised the problem was bigger than "a few bad apples", adding the Met's anti-corruption and abuse command was being encouraged to be "proactive in using more covert techniques".
This included monitoring internal communications "more intrusively where there's good cause", Sir Mark said.
The force is currently reviewing previous allegations of violence against women and girls made against 1,071 Met Police officers and other staff members over the past 10 years.
Sir Mark said some of those officers and staff had "multiple cases" against them.
The review is expected to be completed by the end of March.
Sir Mark also previously announced all 45,000 Met officers and staff would be rechecked for previously missed offending.