British prime minister David Cameron's ex-media chief Andy Coulson will face a re-trial over whether he sanctioned illegal payments to a public official while editing a Rupert Murdoch tabloid.

Last week a jury at London's Old Bailey failed to reach a verdict on whether Coulson and the News of the World'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.

Coulson was, however, found guilty of conspiring to hack into voicemail messages to generate front-page news at the now defunct Sunday tabloid and he is likely to be sentenced later this week.

Three other journalists and a former investigator from the mass-selling paper also pleaded guilty before the trial began and they will be sentenced along with Coulson.

"For a period of years there was industrial scale phone-hacking at the News of the World," prosecutor Andrew Edis said at the opening of the sentencing hearing.

His co-defendant Rebekah Brooks, another former News of the World editor who went on to head the British arm of Mr Murdoch's operation, was cleared of all charges.

The 46-year-old Coulson had edited the now defunct Sunday tabloid between 2003 and 2007. He stepped down after Goodman and the private investigator admitted hacking into phones.

Just months later he went to work as the communications director for Mr Cameron, first in opposition and then in Downing Street when the Conservative leader was elected as prime minister in 2010.

Last week Mr Cameron issued an apology for hiring Coulson which drew criticism from the judge presiding over the trial.

Police said during the trial there were probably more than 1,000 victims of hacking, including Prince Harry, Prince William and his wife Catherine. Politicians, celebrities, sporting figures and even rival journalists were also targeted.

Coulson, who admitted during the trial he had been aware of one hacking incident, said staff had kept the widespread criminal activity from him.

The News Of The World was shut down in disgrace and boycotted by advertisers after it emerged the paper hacked the voicemails of murdered schoolgirl Milly Dowler.

The phone-hacking trial has been one of the most expensive in English legal history.

Reuters