This week, the Leveson Inquiry will hear more evidence about the contact between senior politicians and the Murdoch business, with Prime Minister David Cameron and Chancellor George Osborne among those due to appear.
Hunt endured a bruising session at the inquiry last week, in which he was quizzed on his conduct while reviewing Murdoch's ultimately aborted £8bn takeover bid for the remaining shares in Sky that his News Corp did not already own.
Cameron immediately gave Hunt his backing after the appearance, later saying that the minister had acted "wisely and fairly" in the takeover review.
However, Lord Oakshott, a former Lib Dem Treasury spokesman, told a Channel 4 documentary that "clearly Mr Hunt should have resigned some time ago".
He was interviewed by the Channel 4 Dispatches programme for new documentary Murdoch, Cameron and the £8bn Deal, which airs tonight (June 11).
Lord Oakshott said that "no self-respecting minister could possibly carry on" after it was revealed that Hunt's former special adviser had provided detailed information to News Corp about the handling of the Sky bid.
The Leveson Inquiry also revealed text messages and emails seemingly showing Hunt's support for the bid, even as it was being vetted by the government and regulators.
According to The Guardian, Lord Oakeshott will say in the programme that he got "an increasingly creepy feeling" about News Corp's lobbying over the deal.
He will add that Cameron's unwavering backing for Hunt to remain as culture secretary raised "very serious questions" about the prime minister's judgment, and this suggests a secret deal between the Tories and the Murdoch empire.
"Faustian pacts with the devil - they're not always written down - but it was very clear that a stage came where Cameron and Osborne decided they needed to have Murdoch very firmly on side," he will say on the programme.
Cameron, who has repeatedly denied any such deal, will be able to give his side of the story when he appears at the Leveson Inquiry as the sole witness on Thursday.
Murdoch, Cameron and the £8bn Deal airs on Channel 4 at 8pm tonight.