A British legislator called on Sunday for the country’s media ethics inquiry to publish all the text messages it has between Prime Minister David Cameron and Rebekah Brooks, the ex-chief executive of Rupert Murdoch’s British newspaper division, who now faces charges over the country’s tabloid phone hacking scandal.

The Mail on Sunday newspaper printed two previously unseen messages the pair had exchanged in 2009 on Sunday, prompting a call from opposition Labour Party MP Chris Bryant for Judge Brian Leveson’s ethics inquiry to disclose the texts.

Some messages sent between Mr. Cameron and Ms. Brooks have already been studied by the national panel and released to the public, provoking embarrassment for the British leader. However, other texts which the inquiry says were not relevant to its work have been kept private. Bryant claims the messages have been withheld only because they are “salacious and embarrassing.”

Mr. Cameron, a school friend of Ms. Brooks’ husband, traded text messages with the senior media figure at least once a week and offered her support after she stepped down in 2010 during the hacking scandal. The leader was also forced to acknowledge that he had occasionally gone horse riding with the couple, an image that appeared to reinforce claims by opponents that Mr. Cameron is part of a remote elite.

Mr. Bryant on Sunday urged Mr. Cameron to voluntarily release all messages he had traded with Ms. Brooks. “You can get over being embarrassed, what you can’t get over is deliberately hiding things from the British public,” the MP told BBC.

“We all recognise that that relationship between politicians as a group and newspapers and the media as a group had become too close,” Universities Minister David Willetts, a member of Mr. Cameron’s Conservative Party, said.

Mr. Cameron’s office said that the leader had met all requests made by the media ethics inquiry. “The Prime Minister has always been happy to comply with whatever Lord Justice Leveson has asked of him,” his office said in a statement, referring to the judge running the inquiry.

Giving evidence to the media inquiry in May, Ms. Brooks revealed that Mr. Cameron struggled to understand text message terminology. “Occasionally he would sign them off LOL, ‘lots of love’, until I told him it meant ‘laugh out loud’,” she told the panel.

Ms. Brooks is facing trial next year on conspiracy charges linked to Britain’s phone hacking scandal, which saw Mr. Murdoch close down The News of The World in 2010. She is also charged along with her husband and five other people with conspiracy to pervert the course of justice over allegations she tried to hide information from police investigating the scandal.

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