* Opposition lawmaker quizzes PM in parliament
* Government says it handed over all relevant information
* Inquiry into media ethics reports next month
By Paul Sandle and Mohammed Abbas
LONDON, Oct 17 (Reuters) - David Cameron's friendship with Rupert Murdoch's former British newspaper chief was thrust back into the spotlight on Wednesday when the prime minister refused to answer a question about potentially embarrassing emails between his office and Rebekah Brooks.
Cameron's friendship with Brooks, who has been charged in connection with a phone hacking scandal at one of Murdoch's papers, has already been a source of embarrassment, both politically and personally, for the prime minister.
The opposition Labour party demanded Cameron submit all of the messages between the two to an inquiry into media ethics that is due to report its findings next month after the Independent newspaper reported some had been withheld.
The government, however, said it had provided all the information "relevant" to the inquiry, set up after the disclosures of hacking at Murdoch's now-shut News of the World tabloid and which is looking at the ties between politics and the press.
"We've given the Leveson inquiry everything they wanted," the prime minister's spokesman said. "The relevant information."
Downing Street said it had sought advice from in-house legal experts on what it should provide to the inquiry.
But Labour lawmaker Chris Bryant, who was a victim of phone hacking, demanded to know why Cameron had not published the texts and emails between himself and News International, a unit of News Corp, as well as Brooks and his former media boss Andy Coulson, who used to edit the News of the World.
"Is it because they are too salacious and embarrassing for the prime minister, or is it (...) because there is one rule for the prime minister and another for the rest of us?" he asked Cameron during a question and answer session in parliament.
Cameron ducked the question, saying Bryant had never apologised to him for previously breaking an embargo on information given to the inquiry.
"And you know what, until he apologises, I'm not going to answer his questions," he told parliament.
His angry response did nothing to quell interest in the emails. Opposition lawmaker Diane Abbott tweeted: "What has he got to hide?"
The opposition Labour Party later released a letter urging the prime minister to submit all the communications to Leveson.
"In order for the public to have total confidence it would be preferable for you to disclose all of the emails and let the Leveson Inquiry decide which are relevant," shadow culture secretary Harriet Harman said.
News International was required to submit evidence relating to the company's communications with politicians, but only those that shed light on the relationship between the press and politicians were made public.
The inquiry, headed by a senior judge, has laid bare the close relationship between politicians, the police and the press. When the inquiry reports, one year after it started, Cameron will be faced with difficult choices in dealing with any recommendations on press regulation.
Cameron has already been embarrassed by text messages from Brooks which were aired at the inquiry in which she said they were "professionally in this together".
Another text suggesting they have a "country supper" was analysed for what it said about the two's social status and their friendship, and whether it impacted on government policy and decisions affecting Murdoch's business interests.
She went on to tell Leveson that Cameron signed his frequent text messages "LOL", which he though stood for "lots of love" until Brooks told him it meant "laugh out loud".
A spokesman for the Leveson Inquiry declined to comment on the evidence received.