- NEW: Brooks says she received messages of sympathy from top politicians after resigning
- Her links with Britain's current and former prime ministers are under scrutiny
- She is a former editor of Murdoch's Sun and News of the World newspapers
- The judicial inquiry was set up in the wake of a hacking scandal at the News of the World
London (CNN) -- Rebekah Brooks, a former newspaper editor and News Corp. executive, began testifying Friday over her links to politicians at a U.K. government-backed inquiry into phone hacking and press ethics.
Brooks is likely to face probing questions over her friendship with current Prime Minister David Cameron, as well as her relations with former Prime Ministers Tony Blair and Gordon Brown.
The Leveson Inquiry, set up in response to accusations of widespread phone hacking by journalists working for the News of the World, is currently examining the relationship between Britain's media and politics.
Brooks -- who is known for her close ties to Murdoch -- stepped down as chief executive of News International, the British arm of his News Corp., last summer amid outrage over claims of widespread hacking by staff at its News of the World newspaper.
Brooks told the inquiry she had received some "indirect messages" of sympathy from politicians after she stepped down last summer.
They came from 10 Downing Street, 11 Downing Street, the Home Office and the Foreign Office, she said.
A "very few" Labour politicians sent messages of commiseration, she said.
Blair sent her a message but Brown did not, she said.
Blair's Labour Party benefited from the support of The Sun in three elections.
Brooks was editor of News of the World in 2002 when the newspaper hacked the voice mail of a missing schoolgirl, Milly Dowler, who was later found dead. The hacking scandal led to the paper's closure in 2011.
Brooks then edited The Sun, Britain's biggest-selling daily tabloid, from 2003 to 2009.
Brooks has been arrested twice and released on bail in connection with police investigations into the scandal. She denies any knowledge of phone hacking on her watch.
The ongoing investigations mean questioning on the issue of phone hacking will be limited, so as not to prejudice them or any future trial, and the inquiry will likely focus on her ties to politicians.
She and her husband Charlie Brooks, a racehorse trainer, live near Cameron's constituency home and have socialized with him.
Her testimony about the contacts she had with Britain's current and former prime ministers could prove embarrassing to them if it reveals too close a relationship.
Sky News reported Friday that Blair sent a text message to Rebekah Brooks urging her to apologize ahead of her appearance at parliamentary hearing into phone hacking in 2011.
A spokesman for Blair, Ciaran Ward, told CNN he was not able to confirm whether Blair texted Rebekah Brooks at that point or not, "but if he did he didn't do it in those terms."
Testifying before a parliamentary committee on phone hacking last summer, Brooks said she was aware the newspaper used private detectives but said she had never paid a policeman or sanctioned a payment to the police.
Brooks' appearance at the Leveson Inquiry comes a day after fellow ex-News of the World editor Andy Coulson, who became director of communications for Cameron, took to the stand.
Critics have questioned Cameron's judgment in hiring Coulson after he quit the paper and asked why he was not subjected to more rigorous security vetting.
Coulson resigned as Cameron's spokesman in January 2011 when police opened a new investigation into the scandal. He insisted he was innocent but said he had become a distraction for the government.
Questioned Thursday, Coulson said the jailing of two News of the World employees over phone hacking in 2007 did come up in discussions with senior party members before he was offered the job.
He told the inquiry he had told them and Cameron what he has said repeatedly -- that he knew nothing about the practice of hacking under his leadership of the paper.
He was not asked to give further assurances after more allegations of past misconduct at News of the World emerged while he was working at 10 Downing Street, he said.
Coulson told the inquiry he continued to hold £40,000 ($64,000) of shares in News Corp. while working for Cameron in opposition and in government, but had not considered it a conflict of interest. He had not paid much attention to his financial affairs, he said, because his job kept him very busy.
Coulson said he had told Cameron and then-shadow chancellor George Osborne that his connections to News International would not guarantee the backing of Murdoch's papers.
The Sun switched its allegiance from the Labour Party to Cameron's Conservatives before the 2010 election, which resulted in the formation of a Conservative-Liberal Democrat coalition government.
Coulson said he never witnessed a conversation that was "inappropriate" between members of the government and News International.
He also denied direct involvement in discussions of News Corp.'s bid fully to take over British satellite broadcaster BSkyB, and dismissed as a conspiracy theory the suggestion that some kind of deal had been struck by the Conservatives on that takeover in return for Murdoch's support.
CNN's Laura Perez Maestro contributed to this report.
