The voicemail messages of a murdered British schoolgirl were "most likely" deleted automatically, contradicting a key claim in the News of the World phone-hacking scandal, police told the official inquiry.

Metropolitan Police lawyer Neil Garnham told the Leveson Inquiryinto the ethics, culture and practices of the British press on Monday that it was conceivable that journalists deleted 13-year-old Milly Dowler's voicemails, but police "have no evidence to support that."

He said the "most likely explanation" was that Dowler's service provider automatically removed the messages after 72 hours.

The provider told police that this was "a standard automatic function of that voicemail box system at the time".

Inquiry chairman Brian Leveson said the "significant" new evidence raised questions over the Guardian's story that triggered the scandal, eventually leading to the closure of the Rupert Murdoch-owned title.

Nick Davies, the Guardian reporter responsible for the story, claimed the revelations accurately reflected the view of the police at time and insisted they were still devastating for the News of the World.

"It is delusional to try to pretend that the new evidence on this one element of the story would have changed the outcome," he told Sky News television.

The News of the World's former chief reporter earlier told the inquiry that it had published claims that football icon David Beckham cheated on his wife after deciding it showed his family man image was a sham.

Neville Thurlbeck said that the now-defunct weekly tabloid decided the story was clearly in the public interest.

In 2004, he got the scoop on allegations that England, Manchester United and Real Madrid star Beckham had an affair with his assistant Rebecca Loos.

"We decided there was huge public interest in that matter because the Beckhams had been using their marriage in order to endorse products," he said.

They were making "millions of pounds on the back of that image. It was a wholesome image that the family cultivated and the public bought into on a massive scale and we exposed that to be a sham," Thurlbeck told the inquiry.

He said he spent five months on the story in total, including six weeks in Australia and at least five weeks in Spain, and revealed that Loos received more than £100,000.

"It was the most I think I'd ever paid for a story. We're talking about a six figure sum. Just," he said.

The tabloid was nicknamed the "News of the Screws" due to its numerous sex stories, but Thurlbeck said: "Privacy has become a huge matter over the last three years and I would say the kiss-and-tell story now is largely dead as a genre."

The journalist has been arrested as part of the police investigation into phone hacking at the News of the World. But he has not been charged and the inquiry agreed not to ask him questions on that subject.

The Murdoch tabloid was shut in July following allegations that phone hacking had involved not just celebrities and public figures but also teenager Dowler.

Earlier Mazher Mahmood, the News of the World's ex-investigations editor, told the inquiry he had not been aware of any hacking until the arrest of royal reporter Clive Goodman, who was jailed for the practice in 2007.

Mahmood, known as the "Fake Sheikh" after the disguise he regularly used to dupe targets, rejected previous testimony from Paul McMullan, another former News of the World journalist, that it was a perfectly acceptable tool to expose the truth.

"That certainly doesn't reflect my experience of the News of the World," he said.

Murdoch's news empire is still paying out to victims of phone hacking, and on Monday lawyers for ex-Olympics minister Tessa Jowell said she had accepted £200,000 in damages after she was targeted.