Liberal Democrat deputy leader Simon Hughes has joined calls for an inquiry into whether Culture Secretary Jeremy Hunt breached the ministerial code of conduct.

The senior figure said he could not understand why Prime Minister David Cameron had ruled out referring the controversy over the actions of Hunt's special adviser to a regulator.

Labour claims email contacts between Hunt's special adviser and a News Corp lobbyist about the media group's proposed takeover of BSkyB were in contravention of three parts of the code.

The adviser, Adam Smith, resigned on Wednesday, but Number 10 insists Mr Hunt will answer for his role to the Leveson Inquiry into media standards, which exposed the explosive messages.

It points to a statement from Lord Justice Leveson, asked about the pressure for separate investigations, that "the better course is to allow this inquiry to proceed".

Hunt has asked that his appearance be brought forward.

Deputy Prime Minister Nick Clegg has backed the No 10 stance but Hughes questioned why there should not also be an probe by Sir Alex Allen, the independent adviser on the ministerial code.

"What I cannot understand is why the matter of the ministerial code of conduct, which is to do with do you take responsibility for your special adviser, is not something the Prime Minister should immediately refer to the person who has been given the job of doing that, Sir Alex Alan," he told BBC1's Question Time last night.

A spokesman for Clegg said: "Jeremy Hunt has made his statement to Parliament and will provide more information to the Leveson Inquiry. That process should be allowed to happen."

Hughes broke ranks as Labour maintained pressure for a full investigation into Mr Hunt - who leader Ed Miliband said should be sacked.

The Opposition demanded the publication of emails and text messages between the Cabinet minister and Smith.

Shadow culture secretary Harriet Harman said it was not "credible" that Mr Hunt was unaware of the nature of Smith's contacts with News Corp lobbyist Frederic Michel.

She also raised questions about Hunt's suggestion that the top civil servant at his Department for Culture, Media and Sport, permanent secretary Jonathan Stephens, authorised Smith to act as "point man" with News Corp.

Stephens refused to answer questions on the affair when he appeared before the Commons Public Accounts Committee, but the DCMS said in a statement that he was "aware that Adam Smith was amongst a small number of individuals in the department who were in contact with News Corp and was content with that arrangement".

"As Adam Smith's statement makes clear, the content and extent of his contact was done without authorisation, and were contrary to the clear requirements set out by Jeremy Hunt and the permanent secretary."

Harman demanded publication of those requirements - and emails and texts between Hunt and his special adviser.

Backing for an investigation by Sir Alex also came from senior Tory Bernard Jenkin, who chairs the Commons Public Administration Committee.
There had been a "breakdown of good process and good governance", he told the BBC.

"It is extraordinary that any special adviser should have anything to do with a secretary of state's quasi-judicial role in a matter such as a takeover bid.

"We have a new Cabinet Secretary, Sir Jeremy Heywood, and he should demonstrate his independence and advise the Prime Minister. If he thinks there has been prima facie case of breach of the ministerial code, it should go straight to the independent adviser."

Sir Jeremy spoke to Lord Justice Leveson on the evening of the release of the Michel emails, to inform him that MPs were pressing him for an investigation.

The following morning, the judge said: "Although I have seen requests for other inquiries and other investigations, it seems to me that the better course is to allow this inquiry to proceed."