* Cameron's ex-media chief found guilty of phone-hacking
* Conviction puts British leader under political pressure
* Cameron says sorry, uses press inquiry to avoid questions
* Trial judge criticises Cameron over Coulson comments (Recasts, updates with judge criticism)
By Andrew Osborn and Kylie MacLellan
LONDON, June 25 (Reuters) - British Prime Minister David Cameron came under fire on Wednesday both in parliament and from a senior judge after a court convicted his ex-media chief for being part of a phone-hacking conspiracy.
Opposition lawmakers demanded Cameron explain why he had ignored warnings in hiring Andy Coulson, while the judge who presided over the phone-hacking trial criticised him for commenting publicly on the case before the jury had delivered all its verdicts.
Coulson, who ran Cameron's media operations from 2007-2011, faces a jail term after the jury at London's Old Bailey court found him guilty on Tuesday of the phone-hacking charges.
The conviction for offences committed when Coulson was still a newspaper editor forced the prime minister to make an abject apology on Tuesday for hiring him in the first place, even though the jury was still considering verdicts on two other charges.
With just under a year to go before a national election the opposition Labour party is trying to use the case to argue that Cameron, the leader of the ruling Conservative party, lacks good judgment and doesn't listen to advice from others.
It has criticised Cameron for hiring and retaining Coulson, even though he had already resigned from the News of the World tabloid when two of its employees were jailed in the scandal. Their activity involved the hacking of voicemails left on the phones of celebrities, politicians and crime victims, in the hunt for exclusive stories.
Labour contend that Cameron wanted Coulson in order to curry favour with media tycoon Rupert Murdoch and his British media outlets, which included the now defunct News of the World.
In sometimes heated exchanges in parliament, Labour leader Ed Miliband repeatedly called Cameron's judgment into question, accusing him of disregarding warnings about Coulson from the media and colleagues.
Cameron, he said, did not have any answers to a series of troubling questions about the scandal.
"Today we know that for four years the prime minister's hand-picked closest adviser was a criminal and brought disgrace to Downing Street. We now also know that the prime minister wilfully ignored multiple warnings about him," said Miliband, referring to the British leader's central London office.
Cameron told parliament he was sorry he had hired and then retained Coulson on the basis of assurances that had since been shown to be false.
"I take full responsibility for employing Andy Coulson, I did so on the basis of assurances that I received. I am sorry, this was the wrong decision," he said.
When pressed for more detailed answers, he repeatedly cited a judge-led inquiry into press standards, the Leveson inquiry, which he said had dealt with most of the matters already.
Shouting at times to make his voice heard above the din of jeering lawmakers, Miliband asked Cameron why Coulson had not had proper security vetting, as with previous holders of the job.
British media have said such vetting would have exposed that Coulson had an extramarital affair with Rebekah Brooks, the former boss of the same newspaper he once ran who was acquitted on Tuesday in the trial.
Cameron also faced the wrath of judge John Saunders for making his original apology before the case had fully finished.
"I asked for an explanation from the Prime Minister as to why he had issued his statement while the jury were still considering verdicts," Saunders said in court.
"My sole concern is to ensure that justice is done ... Whether the political imperative was such that statements could not await all the verdicts, I leave to others to judge."
The jury was discharged on Wednesday after failing to reach agreement on whether Coulson authorised illegal payments.
The Dowler family, whose 13-year-old daughter Milly was murdered in 2002, also vented their anger. Milly's voicemail was accessed by News of the World reporters while she was still missing but not confirmed dead.
Her sister Gemma complained of what she called the "incestuous" relationship between top politicians and the British media, saying she was disappointed that Cameron and other politicians had not enforced tougher press regulation.
A new system of self-regulation has since been introduced but many publications have shunned it and critics say it is too soft on newspapers.
"Please keep your promise to us the victims that you will deliver real and permanent change to make sure what happened to us will never happen again," said Gemma Dowler.
Cameron, an expensively-educated politician who is a descendant of King William IV, appointed Coulson in 2007 on the recommendation of George Osborne, now finance minister, to try to bring a more popular touch to his image and policies.
Most analysts believe the political damage to Cameron from the Coulson scandal will be limited.
Speaking before the verdict was pronounced, media commentator Roy Greenslade, a former Murdoch journalist himself, said the embarrassment had already been written into the script.
"It won't renew any pressure on Cameron, everyone knows he made a mistake and that is already factored into peoples' views of him already," Greenslade told Reuters. (Additional reporting by Mike Holden and Kate Holton; Editing by Guy Faulconbridge and David Stamp)