* Andy Coulson convicted last week over phone-hacking
* Jury unable to decide on illegal payments charge
* Four other former Murdoch staff admitted hacking guilt
* Prosecution says they "utterly corrupted" newspaper (Adds quotes, details from hearing)
By Michael Holden
LONDON, June 30 (Reuters) - British Prime Minister David Cameron's ex-media chief Andy Coulson, found guilty last week over phone-hacking while editing a Rupert Murdoch tabloid, will stand trial for a second time over alleged illegal payments, prosecutors said on Monday.
Coulson was convicted by a jury of being complicit in widespread tapping of voicemails by journalists at Murdoch's now defunct News of the World Sunday tabloid following an eight-month trial at London's Old Bailey.
However, the jury was unable to reach a verdict on whether Coulson and the paper's former royal editor, Clive Goodman, were guilty of making illegal payments to a police officer to obtain telephone directories for Britain's royal family. They denied the accusations.
Rebekah Brooks, the ex-chief executive of News Corp.'s British newspaper arm News International who was also tried over phone-hacking allegations and other crimes, was cleared on all charges.
The announcement of the re-trial was made as Coulson and three other senior journalists, who ran the tabloid's news desk and have admitted their role in phone-hacking, appeared in court for a sentencing hearing.
"For a period of years there was industrial-scale phone-hacking at the News of the World," prosecutor Andrew Edis said.
"These defendants utterly corrupted that newspaper which became at the very highest level a thoroughly criminal enterprise."
The 46-year-old Coulson edited the News of the World, then Britain's biggest-selling newspaper, between 2003 and 2007. He stepped down after Goodman and private investigator Glenn Mulcaire admitted hacking into phones of royal aides to generate front page news stories.
Just months later he went to work as the communications director for Cameron, first in opposition and then in Downing Street when the Conservative leader was elected as prime minister in 2010.
Cameron made a public apology following Coulson's conviction, as his political rivals said the appointment had demonstrated the prime minister's lack of judgment.
News International had originally claimed hacking was limited to a "rogue reporter" but increasing numbers of people came forward to say they too had been hacked between 2009 and 2011. The scandal reached a nadir in July 2011 when it was revealed journalists at the paper had hacked the voicemails of murdered schoolgirl Milly Dowler.
Following a new police investigation, three other senior journalists from the tabloid, Greg Miskiw, Neville Thurlbeck and James Weatherup pleaded guilty to being part of a phone-hacking conspiracy before the trial began. Mulcaire also admitted carrying out the hacking of Dowler's phone.
Edis said the names of targets, detailed meticulously in Mulcaire's notebooks, read like a "Who's who of Britain in the first five years of the century," with the years 2005 to 2006 a "golden period" for hacking.
"Politicians, actors, footballers, suspected criminals, actual criminals, indeed almost anybody who appeared in newspapers at this time was represented somewhere in that list.
"In particular names of the royal family and members of the cabinet were targeted."
The maximum sentence for conspiracy to hack phones is two years in prison.
Edis said the estimated prosecution costs for phone-hacking, which could be claimed from the convicted parties, was 750,000 pounds, but it was not clear if News Corp. would be liable for any order made against Coulson.
Coulson went to London's High Court before the trial to ensure News Corp. would pay for his defence bills but it was not clear if they would indemnify him against any court costs, Edis told the judge. (Editing by Kate Holton and Robin Pomeroy)