Downing Street have already released a statement  saying that Mr Hunt will not be investigated over accusations that he was a “back channel” for News Corps in their bid to take full control of BSkyB.

Hunt’s special adviser Adam Smith resigned earlier this week for his connections to the Murdochs, as Hunt took over responsibility of deciding the outcome of the bid.

However, Mr Hughes said on last night’s BBC Question Time that he could not understand why it had not been referred to the independent watchdog.

He said, "What I cannot understand is why the matter of the ministerial code of conduct is not something the prime minister immediately should refer to the person who's been given the job to do it.

"Only the prime minister can do that. He has so far, I gather, resisted doing it. I don't think it gets in the way of the Leveson Inquiry and the evidence - it's a separate matter. I don't know why he hasn't done it but I would have thought, to give confidence in the system, I hope the prime minister reconsiders his view.”

Employment minister Chris Grayling added that we have only heard “half the story” from Mr Hunt, and agreed that an inquiry is needed.

Mr Hunt, despite being responsible for Smith’s actions under the ministerial code, has said that he would not be resigning because he "strictly followed due process".

Meanwhile, News Corps is also under investigation by Ofcom, to decide if it is a fit-and-proper company to hold a broadcasting licence. This could harm their hold over BSkyB even further.