* Ex-British PM offered help at height of hacking scandal
* Email read out at trial of ex-Murdoch CEO Rebekah Brooks
* Blair spokesman says advice was "informal" (Adds background, comments)
By Michael Holden and Kate Holton
LONDON, Feb 19 (Reuters) - Former British prime minister Tony Blair offered to act as a secret adviser to Rupert Murdoch during his media empire's phone-hacking scandal, suggesting the firm follow steps he took to calm public anger over the Iraq war, a London court heard on Wednesday.
Rebekah Brooks, the ex-boss of Murdoch's British newspapers, wrote an email to Murdoch's son James detailing advice Blair had given her during an hour-long phone call in July 2011 at the height of a furore over phone-hacking allegations at the media mogul's News of the World tabloid.
The disclosure came as the prosecution wrapped up its case against Brooks, who is on trial at London's Old Bailey on charges relating to phone-hacking which she denies.
"He (Blair) is available to you, KRM and me as an unofficial adviser but needs to be between us," said the email from Brooks to James Murdoch, who at the time ran News Corp. operations in Britain. KRM refers to Rupert Murdoch's initials.
Brooks said Blair had counselled: "It will pass. Tough up." Four days later she quit her job and she was arrested by police two days after that.
The email was sent the day after News Corp closed the 168-year-old News of the World in the face of huge public anger over revelations that its staff had hacked into the voicemail messages of a murdered schoolgirl.
Blair's suggestions to Brooks contrast with a public statement he made three days before their phone call, when he had denounced the hacking scandal as "beyond disgusting".
The email also demonstrates just how close Brooks and Rupert Murdoch were to Britain's elite, a relationship critics said allowed him to use his British newspapers to influence politicians for the benefit of his business interests.
A spokesman for Blair, who is now a Middle East peace envoy, said the former prime minister was "simply giving informal advice" and had made it clear to Brooks that in a such a serious situation it was vital to have "a fully transparent and independent process" to find out what had happened.
According to Brooks's email, Blair's advice included setting up an internal investigation, led by a member of the "great and the good". The scenario he envisaged was based on the investigation which cleared him of any wrongdoing in the build-up to the 2003 U.S.-led invasion of Iraq.
"Get them to investigate me and others and publish a Hutton style report," Brooks said in the email relaying the comments of Blair, who is godfather to one of Murdoch's children.
"Publish part one of the report at same time as the police closes its inquiry and clear you and accept shortcomings and new solutions and process," the email said.
The reference to the Hutton inquiry could prove hugely embarrassing for the former Labour leader, who won three elections to lead Britain from 1997 to 2007 but who has had to repeatedly defend himself over his decision to join the United States in going to war in Iraq.
Lord Hutton was appointed by Blair to investigate the circumstances which led to the British Broadcasting Corporation (BBC) reporting that the government had "sexed up" the case for the invasion of Iraq.
That near six-month investigation cleared the government of any wrongdoing and laid the blame firmly at the door of the BBC, leading to the resignation of two of its most senior executives. A poll of Britons in the wake of the inquiry found that half believed the report was a "whitewash".
The report was leaked to Murdoch's daily Sun tabloid, which published the findings before its official release in 2004. Brooks was editor of the paper at the time and, despite an official investigation, the leak's source was never discovered.
In May 2012, at an inquiry set up in the wake of the phone-hacking scandal, Blair said British leaders had no choice but to court powerful media barons such as Murdoch or risk savage press attacks from a media he once described as "feral beasts".
The email, which also included a suggestion that Brooks should take sleeping tablets, was read to the jury at the Old Bailey as prosecutors concluded their case against her and six others over phone-hacking and other offences, which they deny.
Another email read out in court from Brooks to James Murdoch detailed a "Plan B" in which they would "slam" other executives and leak an internal report stating that their previous attempts to get to the bottom of the story had been woeful.
Brooks herself had been expected to launch her defence on Wednesday but because of legal issues she is now due to take the stand on Thursday. (Additional reporting by Estelle Shirbon; Editing by Gareth Jones)