* BBC chief takes blame, broadcaster's reputation at stake
* Government says resignation is correct decision
* Criticism grew over sex abuse scandal and false report
LONDON, Nov 11 (Reuters) - BBC director general George Entwistle has resigned just two months into the job, after the state-funded broadcaster aired mistaken allegations of child sex abuse against a former leading politician.
The BBC was already reeling from revelations that a long-time star presenter had been a paedophile, and the conspicuous failure to apply normal journalistic standards was the last thing it needed.
The broadcaster issued a full apology on Friday, but early on Saturday Entwistle had to admit under questioning from his own journalists that he had not known in advance about the Newsnight report, weeks after being accused of being too hands-off over a previous scandal involving the same programme.
By Saturday evening Entwistle was announcing his resignation, saying the unacceptable standards of the Newsnight film had damaged the public's confidence in the 90-year-old BBC.
"As the director general of the BBC, I am ultimately responsible for all content as the editor-in-chief, and I have therefore decided that the honourable thing for me to do is to step down," he said.
Entwistle succeeded Mark Thompson, set to take over as chief executive of the New York Times Co, in September and almost immediately faced one of the biggest crises in the history of the BBC, funded by a licence fee paid by TV viewers.
This was the revelation by rival broadcaster ITV last month that the late Jimmy Savile, one of the most recognisable personalities on British television in the 1960s, 70s and 80s, had sexually abused young girls, some on BBC premises.
Suggestions have surfaced of a paedophile ring inside the BBC at the time, and a cover-up. Police have launched an inquiry and detectives said they had arrested their third suspect on Sunday, a man in his 70s from Cambridgeshire in central England.
Former glam rocker Gary Glitter and comedian Freddie Starr have already been questioned and released on bail.
Entwistle was condemned for the BBC's slow response to the Savile furore and then lambasted after it emerged that Newsnight had axed a planned expose into Savile shortly after his death and that the broadcaster had gone ahead with tributes instead.
His appearance before a parliamentary committee provoked mockery, with one lawmaker saying he had shown a "lamentable lack of knowledge" of what was going on at his own organisation.
Thompson has also had to explain what he knew about the Savile episode and has faced questions from staff at the New York Times over whether he is still the right person to take one of the biggest jobs in American newspaper publishing.
The knives were out for Entwistle on Friday after the BBC apologised for the mistaken allegation that an ex-politician, later identified on the Internet as a close ally of former prime minister Margaret Thatcher, had abused children.
The last straw came when he was forced to admit on the BBC morning news that he had not known - or asked - who the alleged abuser was until the name appeared in social media.
"He showed no sign of being in control the first time (over the Savile issue) and this morning's interview on the Today programme, I think, was fatal, because it happened again," said Steve Hewlett, a media consultant and former BBC editor.
"You could forgive him for the Savile situation, he could have survived that if he'd shown he was on top of this situation, and he didn't," Hewlett told Reuters.
Politicians said Entwistle's decision was right because it appeared that under him the BBC, long affectionately known as "Auntie" and widely respected in many parts of the world, was systematically incapable of addressing its failings.
"It is vital that credibility and public trust in this important national institution is restored," Culture Secretary Maria Miller said in a statement. "It is now crucial that the BBC puts the systems in place to ensure it can make first class news and current affairs programmes."
John Whittingdale, chairman of parliament's powerful media committee, said the crisis had hurt public trust and confidence, and Entwistle's departure did not spell the end of the matter.
"There are still a lot of questions which need answering. Who did take the decision to approve that (Newsnight) programme because quite plainly it was a deeply flawed decision," he said.
The crisis at the BBC is the latest drama to hit the British media industry after two years of soul-searching sparked by a phone-hacking scandal at Rupert Murdoch's newspaper empire.
Any allegations of lack of integrity are serious for a broadcaster that is widely respected and funded by the public. A judge-led inquiry into media standards prompted by the illegality at a Murdoch tabloid is due to be published soon.
Chris Patten, head of the BBC governing body and a prominent political figure, said accepting Entwistle's resignation had made for one of the saddest nights of his public life.
"George has very honourably offered us his resignation because of the unacceptable mistakes and the unacceptable shoddy journalism which has caused so much controversy," said Patten.
"He has behaved as editor with huge honour and courage and would that the rest of the world always behaved the same."
Patten announced that Tim Davie, the BBC's director of Audio and Music, would be the acting director general.