In an outspoken intervention, Lyons, who as head of the BBC Trust worked with Hunt until last year, revealed he had long harboured concerns that the cabinet minister was "far too close" to News Corporation. He poured scorn on the minister's claim that his special adviser, Adam Smith, who resigned last week, had acted in any way without the knowledge of the minister during the proposed BSkyB takeover by News Corp.
In comments likely to raise fresh concerns that Hunt has lost the trust of the wider media industry, Lyons said he did not doubt that there were texts and email messages that connected the culture secretary to his special adviser's alleged collusion with News Corp, at a time when Hunt was supposed to be acting as an impartial judge on the deal.
The prime minister insisted on Saturday there would not be a separate investigation into whether emails and messages between Hunt's office and News Corp provided evidence that the ministerial code had been broken until the minister had given evidence in front of Lord Justice Leveson in about three weeks.
But Lyons, who led the BBC Trust until last May, told the Observer that the culture secretary's explanation of the messages seen by the Leveson inquiry had been "extraordinary". He said: "I have to honestly say that I was surprised [by the revelations] given how much he [Hunt] laboured the quasi-judicial nature of his job, but I wasn't surprised in as much as Jeremy had a very individual way of acting as a minister.
"The notion that seems to have somehow developed that poor Adam Smith might possibly have done this without licence is extraordinary, quite extraordinary. I spoke to Jeremy and Adam Smith in the period immediately after the election and in particular over the runup to the extraordinary accelerated licence-fee negotiations and there is no doubt in my mind that Adam Smith did nothing without Jeremy knowing about it and condoning it. Secondly, that if there is documentary evidence linking Adam, you can be sure that there are texts and phone messages connecting Jeremy because he is not a hands-off minister.
"I don't think he had a very high regard for his civil servants or a strong belief that a minister needed to be particularly bounded by the contribution that the civil servants might make. So he did things very personally."
Lyons added: "A special adviser is trusted in these discussions because they are the direct emissary of the secretary of state and that is what they have historically been used for."
Aides to the culture secretary said the Department for Culture, Media and Sport was going through his phone records and personal email account searching for messages relating to BSkyB, and had found nothing suggesting wrongdoing.
But Downing Street insisted that it would not risk pre-empting the Leveson inquiry by launching an investigation into whether the ministerial code had been broken. Instead, the prime minister's spokesman said an inquiry would only be triggered after Hunt had given his evidence to Leveson if there were grounds to do so. Cameron was standing firm despite Leveson making it clear on Friday evening that he would not be the arbiter of Hunt's probity and amid growing calls for the matter to be referred to the prime minister's adviser on the ministerial code, Sir Alex Allan.
However, concerns about Hunt's conduct are growing. Shadow chancellor Ed Balls accused the culture secretary of misleading parliament for claiming to have been transparent on the BSkyB deal while failing to disclose Smith's communications.
And while Lyons said he did not think it would be "helpful" for him to share his thoughts on whether Hunt should resign, he added that it appeared the minister had paid "scant regard" to the obligations of his office.
He said: "The best I can do is to share my window on that piece of history and to say that I do believe that we are in a healthier environment but it does seem to me that ministers are properly bounded by certain conventions by what they should do and how they should do it and whether they should expose their office to any risk of compromise. A succession of ministers have paid scant regard to those conventions and it is about time it was tightened up."
Lyons, who was chairman at the BBC Trust for four years, including the latest negotiations over the licence fee, added: "We were concerned to avoid what Jeremy Hunt wanted to do, which was a scale and scope review of the BBC, which would have had the secretary of state actually judging how big the BBC is and what things it should do. And part of our concern about that was that we thought he was far too close to Sky."
In other revelations likely to increase pressure on Hunt, the Observer has learned:
■ The culture secretary previously "alarmed" senior figures outside the Department for Culture, Media and Sport with his tendency to carry out discussions through text messages, which are not open to public scrutiny nor covered by the Freedom of Information Act.
■ Lobbyists for the coalition of media companies who were campaigning against the BSkyB takeover were banned by Hunt's officials from attending the only meeting arranged between the culture secretary and the deal's critics while Smith was secretly in contact with News Corp lobbyist Frédéric Michel.
■ The government's green paper on media regulation, due to be published shortly, has been shelved to avoid embarrassment as the scandal over Hunt's conduct unravels.
■ Along with the prime minister and Hunt, it is understood five other cabinet ministers have been called to give evidence to Leveson: the deputy prime minister Nick Clegg, home secretary Theresa May, justice secretary Ken Clarke, business secretary Vince Cable and education secretary Michael Gove.
Writing in the Observer, Lord Puttnam, a former chair of the committee which scrutinised Labour's communications bill, says: "It is now clear that the extent of the secretary of state's prior dealings with the Murdoch empire in opposition and then in government were such as to make it totally inappropriate for him to have been handed political responsibility for oversight of News Corporation's bid for the whole of BSkyB.
""He [Hunt] now finds himself branded as having behaved, not impartially, but more like a dodgy ref, who not only demonstrates bias on the pitch, but ducks into the dressing room at half-time to offer advice."