Mr Staines, who blogs as Guido Fawkes, told the Leveson Inquiry he had heard the claims from two journalists.
The blogger made the comments as part of questioning into why he was not prepared to join any regulatory body.
"Tina Weaver, somebody who two journalists have told me has personally authorised and told them to hack, blag and do all that kind of stuff, sits on not just the PCC, but on the ethics committee, the editorial standards committee.
"She knows all the bad things that have gone on under her rule. It's ridiculous."
Mr Staines said Lord Hunt of Wirral, chairman of the Press Complaints Commission (PCC), had been trying to woo him to join a kitemark system but he did not think that was "a road" he would go down.
Asked why not, he said: "If I joined any regulatory body I would end up in a system where I am going to have to self-censor and I don't want to do that.
"I also don't want to have an editorial product that is politically correct and I don't want to have to adhere to standards that Harriet Harman would adhere to.
"I don't think there are many publishers around now, not even Private Eye, who are still politically incorrect in the way that we are."
Ms Weaver has previously told the inquiry she was not aware of phone hacking at her newspaper but there was no guarantee that it had not occurred.
She was asked about a BBC article which claimed there was routine phone hacking in the newsroom of the Sunday Mirror.
She said her organisation was "not happy" about the story which contained "anonymous allegations from seven years ago".
Counsel for the inquiry David Barr asked her if it was her position that there was "no guarantee" that phone hacking had not occurred at the newspaper.
She replied: "That is correct."
Mr Staines told the inquiry his blog broke a story about William Hague sharing a hotel room with a male political adviser and gave pictures of the adviser to the News of the World for £20,000.
He said the pictures were never published.
"You don't buy pictures for £20,000 not to publish them. It was at the point of the building tensions with Andy Coulson and Downing Street, matters were about to come out and perhaps to curry favour they chose to buy up those pictures and then not publish them."
Mr Staines told the inquiry "lobby" journalists were well aware of the expenses scandal before the story was in the public domain.
"Lobby journalists were aware of the system and perfectly understood what was going on but they just accepted it."
He said the only reason the scandal came out was because of the work of freedom of information campaigner Heather Brooke.
He told the panel that the political lobby functions like "an obedience school for journalists", with press officers denying journalists access for unfavourable coverage.
He said the strict rules of the lobby, known as "lobby terms" went beyond "off the record" and made journalists complicit in deceptions.
"If a politician tells a lobby journalist he believes the sky is blue and (the politician) then goes on Newsnight and says he believes it is red, he cannot report he is lying to the public.
"That is not just off the record, you have journalists complicit in politicians lying when they could reveal the truth."
He said Parliament denied journalists access if they did not comply with lobby terms and journalists went along with this because it was "a cartel", adding "I don't think it is a healthy system."
He said a way to improve the system would be to televise lobby briefings because they are often used to besmirch others.
He said: "There is nothing magical about them. Most people would probably find them quite boring."
He added that there was currently a "trade in favours" and said journalists should not accept anonymous briefings.
"It is standard technique for press officers to give titbits to their favourite journalists for favourable stories about their principal."
He said if their principal received unfavourable coverage they would be denied access and this was a particular problem for broadcast journalists because their reports are made far more interesting when there are interviews with key politicians.
Mr Staines claimed his own phone number and address had been obtained by Daily Telegraph reporter Gordon Rayner, and told the inquiry it could only have been achieved through asking someone at the Land Registry to pass on his details.
He claimed Mr Rayner had used private detective Steve Whittamore, who was convicted of illegally accessing data in April 2005.
The inquiry has heard a search of Mr Whittamore's office in March 2003 by the Information Commissioner's Office (ICO) as part of Operation Motorman uncovered a "treasure trove" of evidence linking newspapers to the sale of private data.
Mr Staines claimed Mr Rayner's name appeared in Operation Motorman files 335 times, saying 185 related to alleged illegal transactions.
"If this inquiry does not act as a catalyst for criminal prosecution for those journalists who have invaded people's privacy, on an industrial scale, I think you have failed," Mr Staines said.
The blogger told the inquiry the evidence behind his claims about Ms Weaver came from journalists telling him she had told them to "spin" a phone.
He said comments he had previously made about former News of the World editor Piers Morgan were "derived" from his own writing.
Mr Staines was also asked how he came by a copy of Alastair Campbell's witness statement to the inquiry.
Tony Blair's former communications director's draft statement was published online by Mr Staines early in the inquiry.
The leak prompted Lord Justice Leveson to make an order banning advance publication of documents submitted to his team.
Mr Campbell has previously told the inquiry he gave drafts to various people but was confident none of them would have passed it to Mr Staines.
Mr Staines said today: "I don't know the exact mechanics... but my source was a journalist and I believe that he obtained it from another journalist."
In his written statement, Mr Staines told the inquiry there was a danger that privacy laws would end up sparing the embarrassment of celebrities rather than protecting human rights.
He said: "The public interest will not be well served by privacy laws which will effectively create judicial censorship.
"The privacy laws currently being made from the bench in English courts are a travesty of the intentions of the original drafters of the European Convention on Human Rights.
"They had in mind protecting the human rights of individuals from
oppressive states and agencies of those states. They did not have in mind sparing the blushes of footballers caught having extra-marital affairs or celebrities who have exotic tastes in the bedroom or dungeon."
He added: "The popular press is in danger of being shackled by privacy laws and 'media standards' which are really a euphemism for censorship.
"This will undermine the popularity and commercial viability of newspapers, inevitably doing damage to media plurality in the long term."
He added that the BBC is the biggest threat to media plurality with a dangerous dominance of news because of its size and method of funding.
Among other witnesses, Sir Paul McCartney's ex-wife, Heather Mills, is to give evidence to the inquiry tomorrow morning.
Daily Mail editor Paul Dacre will also return to answer questions on about claims made by actor Hugh Grant.
Prime Minister David Cameron set up the Leveson Inquiry
last July in response to revelations that the News of the World commissioned a private detective to hack murdered schoolgirl Milly Dowler's phone after she disappeared in 2002.
The first part of the inquiry,
sitting at the Royal Courts of Justice in London, is looking at the culture, practices and ethics of the Press in general and is due to produce a report by September.
The second part, examining the extent of unlawful activities by journalists, will not begin until detectives have completed their investigation into alleged phone-hacking and corrupt payments to police,
and any prosecutions have been concluded.
PA
