Jeremy Hunt investigation rejected by watchdog The Prime Minister insisted the decision over whether the launch an investigation was his alone but told MPs he had received a letter from Sir Alex Allan, independent adviser on ministerial interests, backing his claim that the Leveson Inquiry hearing dealt with the issue. Mr Cameron also dismissed Liberal Democrat plans to abstain in a vote being forced by Labour on the issue today as "politics." Deputy Prime Minister Nick Clegg, who was absent from prime minister's questions because he was giving evidence at the Leveson Inquiry, has repeatedly told Mr Cameron he believed Sir Alex should be brought in to consider the case. Labour leader Ed Miliband said the Prime Minister was in a state of "delusion." Sir Alex said the decision over whether a case was referred to him was a matter for Mr Cameron, adding he "remains available." His letter states: "The fact that there is an ongoing judicial inquiry probing and taking evidence under oath means that I do not believe I could usefully add to the facts in this case though I remain available should circumstances change or new evidence emerges." Earlier this year the public administration select committee published a critical report about the lack of power Sir Alex's role holds. It called for changes that would allow the independent adviser to embark on investigations without referral from the Prime Minister. Labour dismissed Sir Alex's letter as a "smokescreen." A senior Labour spokesman said: "This is a David Cameron smokescreen. It is not an effective one. The questions are about the Prime Minister's judgment. We know what the facts are. We know he has failed to exercise proper judgment. Downing Street said Mr Cameron wrote to Sir Alex this morning, ahead of his appearance before the Leveson Inquiry tomorrow, and received an immediate reply. Mr Cameron is expected to use his appearance before Lord Justice Leveson to give details of the changes he is considering to the guidance for ministers, which will set out how they should behave when exercising quasi-judicial authority in a legal matter. In his letter, Mr Cameron told Sir Alex: "As you know, I have decided not to refer Jeremy Hunt to you as I am satisfied that the relevant information about this issue has been established and I am content that he did not break the ministerial code. Separately, I will be outlining to Lord Justice Leveson some of the initiatives this Government has taken to strengthen accountability and transparency as well as some areas where I am proposing future changes to the current guidance. These include the conduct of special advisers and the handling of quasi-judicial decisions and I would welcome your comments. Mr Cameron said it was the job of the Prime Minister to make any judgement about whether the ministerial code had been breached. "I've made that judgment," he added. Sir Alex Allan is very clear that he couldn't usefully add to the facts of the case. But Mr Miliband insisted a memo Mr Hunt sent to the PM about the bid before he took over responsibility for it showed he had misled parliament when previously telling MPs he had made no intervention seeking to influence the process. The Labour leader added: "The truth is you won't refer him to the independent adviser because he is scared the Culture Secretary won't be cleared." Mr Clegg's decision to direct his MPs to abstain on the Labour motion, which calls for Sir Alex to investigate whether Mr Hunt misled Parliament and failed to take responsibility for his special adviser Adam Smith, who resigned after admitting his contacts with News Corporation had been too close, has laid bare coalition tensions. "I don't think the Prime Minister was pleased about it," party sources said. Pressed about the decision, Mr Cameron said: "Let me be absolutely frank, what we are taking about here is the relationships Conservative politicians, and frankly Labour politicians, have had over the last 20 years with News Corporation, News International and all the rest of it. To be fair to the Liberal Democrats they didn't have that relationship and their abstention tonight is to make that point and I understand that. It's politics. Mr Miliband said that the key question now was about the Prime Minister's judgment in deciding to appoint Mr Hunt in 2010 to oversee the bid by News Corporation to take over satellite broadcaster BSkyB, despite his previous public expressions of sympathy for the £8 billion deal. The Labour leader told MPs: "The reality is this - everyone knows it was the Prime Minister who decided to appoint the Culture Secretary to oversee the bid and the Prime Minister who is clinging on to him now in the face of all the evidence. It is no longer about the Culture Secretary's judgment. It is about the Prime Minister's judgment, which is so deeply flawed even his deputy won't support him. Mr Cameron said his Labour predecessor Gordon Brown should consider releasing Downing Street phone records in order to clear up a contradiction between his evidence to the Leveson Inquiry and that of News Corporation boss Rupert Murdoch. Mr Murdoch told the inquiry Mr Brown made an "unbalanced" call to him in September 2009, after The Sun had declared support for the Conservatives in the upcoming general election, in which he said he was "declaring war" on the media company. Mr Brown this week denied that the conversation took place, and said he was "shocked and surprised" by Mr Murdoch's account. Downing Street has confirmed that written notes are routinely taken by the PM's private secretary of official phone calls, though they is not normally a tape recording or verbatim transcript. However, incoming administrations are not permitted to release the records of a previous government. Mr Cameron told MPs: "Governments can't release information provided by previous governments, but I am sure this is an issue that the previous prime minister will want to consider, given the very clear statement that he made." Aides confirmed that Mr Cameron has consulted a Government QC and the Treasury solicitor while preparing for tomorrow's appearance at the Leveson Inquiry. One source close to the PM said: "I don't think he is nervous, but it is a very serious thing, so you would expect him to be doing preparation."