The Chancellor, George Osborne, has become the latest minister to be dragged into the BSkyB takeover scandal as evidence emerged suggesting that he played a behind-the-scenes role in the Government's handling of the £8bn bid.

Records retrieved from the phone of the Culture Secretary, Jeremy Hunt, show him and Mr Osborne exchanging text messages in the hours after anti-Murdoch remarks by Vince Cable were made public. Mr Hunt texted the Chancellor asking to talk about the takeover, saying he was "seriously worried we are going to screw this up". Mr Osborne texted back: "Hope you like the solution" – and then Mr Hunt was handed responsibility for deciding on the bid.

The revelation makes it more likely that Mr Osborne will be made to give evidence to the Leveson Inquiry and have to reveal the contents of his own texts and emails exchanged with the Murdoch empire. Other emails released yesterday show the depth of concern both in Downing Street and in Mr Hunt's own department about whether the Culture Secretary's previous noisy support for the Murdochs was clear evidence of bias and must rule him out of handling the deal. Mr Hunt can be seen emailing the Prime Minister's chief of staff in the hours after the row broke out.

Yesterday, David Cameron made clear he was staking his reputation on Mr Hunt being cleared by the Leveson Inquiry after the Culture Secretary gave more than five hours of evidence explaining his handling of the bid. Downing Street said the Prime Minister had no intention of calling an inquiry into whether Mr Hunt had broken the Ministerial Code and dismissed Labour claims that the Culture Secretary had misled Parliament.

But the position relies on Lord Justice Leveson agreeing that Jeremy Hunt was not aware of the extent and nature of the contact between his special adviser Adam Smith and the News Corp lobbyist Fréd Michel when he produces his final report.

Mr Cameron will also come under pressure from Labour who last night said it was deplorable that Mr Hunt would not face a government investigation under the code.

"David Cameron should never have given the decision to Jeremy Hunt in the first place, because he was clearly already biased," said Labour's deputy leader, Harriet Harman. In other developments yesterday it also emerged that:

* Mr Hunt texted James Murdoch – hours before he was given responsibility for BSkB bid – congratulating him on European clearance for the takeover. "Just Ofcom to go," he wrote. Mr Hunt accepted he was "supportive" of the takeover before being given responsibility for it but insisted he "set aside any views" he had in his quasi-judicial role.

* Mr Hunt exchanged private messages with Mr Murdoch even once he was in the new judicial role. In March he sent Mr Murdoch a message congratulating him on his new job at News Corp headquarters in America.

* At no stage during his time in office had Mr Hunt used an official government email. All correspondence went through his own Gmail account – inaccessible to his civil servants.

But it was the sequence of events on 21 December 2011 – the day Mr Hunt was given responsibility for the bid – that causes the greatest difficulty for the Government. Records from Mr Hunt's phone show he sent Mr Osborne a message after receiving a phone call from James Murdoch questioning the legitimacy of the process. Timed at 4.08pm, Mr Hunt's message to Mr Osborne read: "Could we chat about Murdoch Sky bid? I am seriously worried we are going to screw this up. Jeremy."

A couple of minutes later, Mr Hunt sent an email to Andy Coulson, the former News of the World editor at that time working as Mr Cameron's director of communications: "Could we chat about this? I am seriously worried Vince Cable will do real damage to coalition with his comments."

At 4.58pm, with the formal appointment of Mr Hunt to take over examination of the takeover bid to be announced within the hour, the Chancellor replied by text to Mr Hunt: "I hope you like the solution."