Boris Johnson has said the government will “stop at nothing to make sure that we get more rapists behind bars” in the wake of the murder of Sarah Everard.

The prime minister said he wanted to have “more successful prosecutions for rape and for sexual violence”, adding: “Because that, I think, is going wrong.”

Ms Everard was kidnapped, raped and murdered by Wayne Couzens, who was a serving police officer when he carried out the killing of the 33-year-old marketing executive in March.

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Couzens, who strangled Ms Everard with his police belt after kidnapping her under the guise of an arrest, was handed a whole life order at the Old Bailey earlier this week.

Questions have been raised about police vetting procedures after it was revealed that Couzens was linked to a flashing incident in 2015, and two more incidents days before he killed Ms Everard.

In addition, the police watchdog is investigating five officers over claims they traded misogynistic, racist, and homophobic material with Couzens over WhatsApp months before he killed Ms Everard, according to a report in The Times.

Speaking to Sky News, a former senior Metropolitan Police chief superintendent said every police officer in the UK should be re-vetted.

In an interview with the BBC’s Andrew Marr Show on the first day of the Conservative Party conference in Manchester, Mr Johnson dismissed calls for an immediate independent public inquiry.

He said investigations by the Metropolitan Police and the Independent Office for Police Conduct should be allowed to run their course.

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The PM added: “We do need to look systemically at not just the Wayne Couzens case but the whole handling of rape, domestic violence, sexual violence and female complaints about harassment all together.”

He also backed advice from the Met Police for women to flag down a passing bus if they are stopped by an officer they do not trust.

The advice, which has drawn heavy criticism, also included suggestions to shout, knock on doors or call 999.

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“If you are suspicious about the way in which you are being treated by a police officer and you are worried for some reason, then clearly you should seek help in the way you have described,” Mr Johnson told the BBC when asked about that advice.

“My view is that the police do – overwhelmingly – a wonderful job and what I want is the public, and women in particular, girls and young women, women of all ages, to trust the police.

“They are overwhelmingly trustworthy.”

Are women safe on our streets?

The murder of Sarah Everard by a serving Metropolitan Police officer has resulted in an outpouring of concern over women’s safety in the UK.

We would like you to share your experiences, and your questions for our panel of experts. We’d also love to hear your solutions.

Email thegreatdebate@sky.uk to get involved.