By Michael Holden and Kate Holton

LONDON (Reuters) - Rebekah Brooks, a former top editor, and Andy Coulson, Prime Minister David Cameron's ex-media chief, oversaw a system of phone-hacking and illegal payments when they ran Rupert Murdoch's British tabloids, a London court heard at the start of their trial on Wednesday.

Setting out the prosecution case, Andrew Edis said Brooks was linked to both phone-hacking that ruined the tabloid News of the World and the practice of paying public officials for stories at its sister newspaper, the Sun. Brooks, 45, later ran Murdoch's British newspaper division from 2009 to 2011.

Edis said that Coulson, who helped guide Cameron into the prime minister's office in 2010, was Brooks's deputy and later ran the News of the World, a Sunday paper, when its staff routinely hacked or ordered the interception of voicemail messages of well-known figures and people close to them.

They both deny the charges.

Among alleged targets identified were model Kate Moss; Frederick Windsor, the son of Queen Elizabeth's cousin; Beatle Paul McCartney; and Louise Woodward, a British au-pair jailed by a U.S. court for the 1997 killing of a baby in her care.

Edis told the jury at the beginning of the high-profile trial in London's Old Bailey court that it was now beyond doubt phone hacking had occurred at the muck-raking News of the World and the jury now had to decide how far the conspiracy went.

"We can prove there was phone hacking and quite a bit of it," he said, as both Coulson and Brooks stared ahead or took notes in the dock of what is expected to be a six-month trial.

"The prosecution says journalists are no more entitled to break criminal law than anybody else."

Revelations about phone-hacking stunned the top echelons of the British establishment and engulfed Murdoch's News Corp empire during the summer of 2011, forcing the media mogul to close the 168-year-old News of the World.

Brooks and Coulson, two of Britain's most high-profile former newspaper editors, are accused of conspiring to hack phones and make illegal payments. She also faces two counts of conspiracy to pervert the course of justice.

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Six others including senior figures from Murdoch's British newspaper arm, then known as News International, and Brooks's husband Charlie are also on trial, and all deny the charges.

Edis said Brooks had sanctioned illegal payments to public officials, including one for nearly 40,000 pounds ($64,000) to a senior Ministry of Defense official.

Coulson, 45, is accused of authorizing a payment to a royal police protection officer to secure a phone book with contact details for royal staff, an important tool for those wanting to hack phones, the court heard.

When police finally began to reveal the truth, Brooks and her husband, both close friends of Cameron, along with other News International figures mounted a cover-up by trying to dispose of old notebooks and computers, Edis said.

MILLY DOWLER

The issue of phone-hacking first came to light in 2007 when News of the World royal editor Clive Goodman and private detective Glenn Mulcaire were convicted of hacking phones belonging to an aide to princes William and Harry.

Edis said Mulcaire, an accomplished "blagger" and phone hacker, had now pleaded guilty to further charges of hacking phones including that of Milly Dowler, a schoolgirl who went missing in 2002 and was later found murdered.

It was news of the Dowler hack in 2011 that "brought down the News of the World", Edis said.

The court heard three former senior journalists from the News of the World - Neville Thurlbeck, James Weatherup and Greg Miskiw - had also admitted conspiracy to hack phones.

Their guilty pleas, which had not previously been reportable, were the first admissions by former staff from the tabloid since police relaunched their inquiry in 2011.

"It can never be suggested now by anybody that phone hacking was restricted to Mr Goodman," Edis said.

The prosecutor argued that Brooks and Coulson must have known about the hacking since the News of the World had been paying out about 100,000 pounds a year to Mulcaire and they held the paper's purse strings.

"If these people were doing their jobs properly, we say they must have known where these stories came from, otherwise they would never have got in the paper," Edis said.

"Or at least three or four of the newsdesk editors were running this operation with Mr Mulcaire doing this great deal of phone hacking without their managers knowing. Well, what on earth were they doing?"

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(Additional reporting by Joshua Franklin, editing by Stephen Addison and Mark Heinrich)