Former News International chief executive Rebekah Brooks discussed phone hacking allegations with David Cameron, the Leveson Inquiry has heard.

The former News International chief executive said she had spoken about the scandal with the Prime Minister on a few occasions between 2009 and 2011 in general terms, and after the Guardian reported missing teenager Milly Dowler’s phone had been hacked on behalf of the News of the World.

Brooks told the inquiry Cameron, George Osborne and Tony Blair had commiserated her following her resignation from the company last year. Both Cameron and Blair attended Brooks’ 40th birthday party, thrown by Rupert Murdoch.

She said: “The phone hacking story was a sort if constant, or it kept coming up. We would bring it up but in the most general terms. Maybe in 2010 we had a more specific conversation about it.

“I think it was nothing particularly that he wouldn’t have said publicly, but he was interested in the latest developments and asked me about them and I said to him what I say to everybody when they asked me for an update on it. It was to do with the amount of civil cases coming in around 2010 and we had a conversation about it."

She denied rumours Cameron texted her 12 times a day, saying it was around once a week - twice a week during the 2010 election campaign - and said the messages concerned organising meetings, social occasions and occasionally personal comments.

She added: “[Cameron] would sign them off “DC” in the main. Occasionally he would sign them off “LOL”, actually until I told him it meant “laugh out loud” and then he didn’t sign them like that anymore.”

When asked about News Corporation’s BSkyB bid, Brooks said she had an informal role in lobbying but was not involved in the proposed deal or the strategy behind it. She confirmed evidence given by James Murdoch, who said the bid had been briefly discussed at a dinner with Cameron in 2010, and admitted personally discussing the bid with both the Prime Minister and Osborne.

Brooks admitted having a close personal relationship with Rupert Murdoch, but denied politicians sought access to the proprietor by getting close to her, saying her personal relationships were all appropriate.

She told the inquiry: “I mean we all have lots of different friendships. Old friends, new friends, work colleagues, associates. And through the decade that I was a national newspaper editor, the years I was a CEO and the ten years I was a journalist, some friendships were made. But I don’t think I ever forgot I was a journalist and I don’t think they ever forgot they were a politician.”

Brooks was asked about former prime minister Gordon Brown, who she claimed called to complain after the Sun criticised him for sending a poorly-spelled letter to the mother of a recently deceased soldier. Rupert Murdoch has previously told the inquiry Brown rang him to discuss the Sun’s decision to support the Conservatives in the 2010 election.

Brooks said Brown had shown “extraordinary levels of aggression” as she reassured him she had spoken to Sun editor Dominic Mohan and the Sun’s coverage would not be a series of personal attacks. She told the inquiry earlier Brown “was probably getting the bunting out” when her resignation was announced.

She said: “Previous to that conversation, I had also indirectly had similar – not threats made but similar sorts of comments made about the Sun abandoning Labour after 12, 13 years - hostile comments. So when Mr Murdoch told me his conversation, it didn’t surprise me.”

She added: “I don’t think its fair to say that politicians live in fear of newspapers, they are highly-motivated, ambitious people, and MPs don’t scare easily.”

Brooks said her relationship with Brown became fraught after the Sun took the side of Blair over the infamous “curry shop coup”, the attempt of some Labour politicians to out Blair as prime minister.

She told the inquiry: “It wasn’t a playground spat, they were the Prime Minster and the Chancellor of the Exchequer. We were a newspaper who was looking after the real serious concern of our readers. So it wasn’t that I would stand on one corner of the playground and [Guardian editor] Alan Rusbridger would stand on the other... and it would be he was on Gordon’s side and I was on Tony Blair’s, it just didn’t work like that."

Brooks said the timing of the Sun’s decision to back the Conservative Party in 2009 was decided between her, Mohan, the paper’s political team, and James and Rupert Murdoch, denying Cameron and his advisors had a role in the timing of when the support would be announced. James Murdoch told Cameron of the shift in September 2009.

She admitted disagreeing with Murdoch during her time as editor of the Sun, on several issues including the amount of celebrity coverage in the paper, but said they spoke “very frequently”.

She added: “You only have to look at the viewing figure of the BBC or ITV to see that it’s the celebrity programs, the reality programs that do so well, and I took from those figures that our readers were quite interested in that. He thought there was too much of it, although he liked the X Factor.”

Asked about Rupert Murdoch’s comment to reporters that the CEO was his priority in the hacking scandal, Brooks said she was not embarrassed at the time because she believed he was referring to the issue rather than her personally.

She told the inquiry: “He was being asked by many reporters lots of different questions, and I think someone said ‘what is your priority’ and he looked towards me and said ‘this one’. I took that to mean he meant as in this issue. It was only the next day when I saw how it could have also been interpreted in the papers that I realised that was the interpretation that had been put on it. I wasn’t embarrassed at the time because I didn’t know that that’s what he meant."

Brooks continues to give evidence this afternoon.