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The Metropolitan Police commissioner said the force was investigating 1,000 sexual and domestic abuse claims involving about 800 of its officers.
It comes after Met officer PC David Carrick pleaded guilty to 49 offences, including dozens of rapes.
A spokesman for the prime minister said high-profile cases such as Carrick’s had “shattered” the public’s trust in policing.
Sir Mark Rowley apologised to Carrick’s victims for the force’s failings.
“We have failed. And I’m sorry. He should not have been a police officer,” he said.
Sir Mark said: “This man abused women in the most disgusting manner. It is sickening. We’ve let women and girls down, and indeed we’ve let Londoners down. The women who suffered and survived this violence have been unimaginably brave and courageous in coming forward.
“I do understand also that this will lead to some women across London questioning whether they can trust the Met to keep them safe.
“We haven’t applied the same sense of ruthlessness to guarding our own integrity that we routinely apply to confronting criminal.”
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‘Breach of trust’
Home Secretary Suella Braverman said it was a “sobering day” for the Met and “the whole policing family throughout the country”.
“This appalling incident represents a breach of trust, it will affect people’s confidence in police and it’s clear that standards and culture need to change in policing.
“This appalling incident represents a breach of trust, it will affect people’s confidence in the police and it is clear that standards and culture need to change in policing.”
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She said chief constables needed to follow recent guidance by HM Inspectorate of Constabulary on prioritising vetting and recruiting processes.
“I expect every chief constable to take on board those recommendations and implement them urgently,” she said.
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