The BBC has been plunged into the deepest crisis in its history with the dramatic resignation of its director general, George Entwistle, after just 54 days in the job.

Entwistle fell on his sword after being engulfed by a crisis that escalated following confirmation on Friday that the BBC had wrongly implicated Lord McAlpine, a former senior Tory politician, in a story about paedophilia. It was the second scandal to hit Newsnight in recent weeks.

In an extraordinary scene outside Broadcasting House, in central London, just after 9pm, Entwistle, flanked by the BBC Trust's chairman, Chris Patten, said he felt it was the "honourable" thing to do.

His resignation was accepted by Lord Patten who said it was one of the "saddest evenings of my public life" to see Entwistle end his 23-year career at the BBC in such ignominious circumstances.

Looking composed, but battle-weary, Entwistle read from a prepared statement: "In the light of the fact that the director general is also the editor in chief and ultimately responsible for all content; and in the light of the unacceptable journalistic standards of the Newsnight film broadcast on Friday 2 November, I have decided that the honourable thing to do is to step down from the post of director general," he said.

Tim Davie, currently director of audio and music who was scheduled to take over as head of BBC Worldwide, was named as the acting DG while the hunt for a new boss takes place.

Entwistle's resignation came less than 12 hours after a catastrophic interview with John Humphrys on Radio 4's Today programme in which Entwistle admitted he was completely unaware that Newsnight was going to make such serious allegations about a senior Tory politician. Critics said he gave the impression of a man completely at sea when he admitted that not only was he unaware of the allegations, but that nobody had brought to his attention an article in Friday's Guardian that the victim of child abuse in the Welsh care home, Steve Messham, who had made the claims, may have mistaken the identity of the perpetrator.

The pressure on Entwistle intensified on Friday morning when McAlpine broke cover after eight days of rumour and innuendo going viral on Twitter, branding the allegation as entirely false and threatening to sue the BBC.

John Whittingdale, the chairman of the influential select committee that grilled Entwistle over the Jimmy Savile scandal, said he thought Entwistle had made the right decision as his "position had become untenable, once he had said he was unaware that the programme was being broadcast". He told BBC News: "It left the impression that the management of the BBC had lost their grip on the organisation and I think the decision is undoubtedly the right one."

BBC director generals have resigned in the past, but none has risen and disappeared within such a short space of time. On Saturday afternoon Jonathan Dimbleby, one of the corporation's best-known broadcasters, said he feared the public now perceived the BBC as "a rudderless ship heading towards the rocks", adding he hoped somebody would "seize the helm quickly".

Culture secretary Maria Miller said Entwistle had made the right decision: "It's a regrettable situation, but the right decision. It is vital that credibility and public trust in this important national institution is restored. It is now crucial that the BBC puts the systems in place to ensure it can make first class news and current affairs programmes."

Sir Christopher Bland, a former chairman of the BBC board of governors, said: "It's arguable that it's a necessary sacrifice, but it's tragic for George and tragic for the organisation."

Newsnight presenter Jeremy Paxman issued a statement describing Entwistle's departure as "a great shame" and accusing "cowards and incompetents" of bringing about his downfall.

He blamed a culture of caution at the BBC in the wake of the 2003 Hutton inquiry and a management that had become bloated at the expense of programme budgets. "I had hoped that George might stay to sort this out. It is a great pity that a talented man has been sacrificed, while time-servers prosper."

Humphrys, meanwhile, offered a pithy comment about his role in the director general's demise. "Let it settle down. I am not going to gloat. I do what I do. I did what I did," he said.

Michael Crick, the former Newsnight political editor, who was instrumental in revealing the mistakes made in the recent investigation into false claims concerning Lord McAlpine, tweeted: "George Entwistle's resignation v sad. A good, decent man, badly let down. V few people could have coped with recent rush of awful events." Former Labour culture secretary Ben Bradshaw tweeted his unhappiness that Entwistle had been "forced" out, describing it as a "terrible mistake".

Enwistle was appointed as director general this summer and took over from Mark Thompson in September, but within two weeks he was hit by the extraordinary revelations that Jimmy Savile, one of the BBC's biggest stars, had been a serial child abuser and had molested underage girls on BBC premises. He was immediately put on the back foot when it emerged that the BBC had quashed a Newsnight investigation into Savile last December, just weeks before three tribute programmes were due to be scheduled.

Entwistle had been warned that it might cause a problem, but had failed to inquire what the subject of the investigation was, leading to criticism that he displayed "an extraordinary lack of curiosity" about his own organisation.

The Humphrys interview in which Entwistle admitted for the second time that he did not know anything about the content of a controversial Newsnight programme compounded the apparent lack of judgment, with politicians lining up on Saturday to question whether he was the right man for the job.

Bland added that the BBC now needed to establish "calmly and accurately what went wrong" to safeguard against future blunders. He said it was extraordinary that the "bog standard checks" had not been made by Newsnight – the programme-makers had not contacted McAlpine about the allegations or shown a photograph of McAlpine to Messham, the victim of child abuse who made the accusations.

He said serious questions needed to be asked of other executives. "Where were the lawyers; where was the chain of command?"

Bland also accused others, including writer George Monbiot, Sally Bercow, the wife of the speaker of the House of Commons, and Tom Watson, the Labour MP, of irresponsible behaviour for circulating McAlpine's name on Twitter.

Senior insiders say the mistakes were made because the Savile scandal had effectively torpedoed the management structure in BBC news and current affairs with senior executives, including the head of news and the editor of Newsnight, standing down from their posts while two internal inquiries took place.

One senior journalist said the chain of command was now "breakable brittle rubber" rather than the rod of iron normally in place which would ensure the highest editorial standards in the world.