Embattled Culture Secretary Jeremy Hunt is facing a lengthy wait to defend himself at the Leveson Inquiry after his request for an early appearance was rebuffed.

Lord Justice Leveson has refused to bring forward Hunt's appearance so that he can answer allegations about his handling of News Corporation's BSkyB takeover bid.

A date has still not been set, but politicians will not be called until mid-May, meaning the Culture Secretary will have to wait at least a fortnight and possibly much longer.

It is also thought that Lord Justice Leveson will not rule on whether Hunt breached the ministerial code, piling additional pressure on David Cameron to order a separate inquiry.

Lord Justice Leveson's response is a setback for the under-fire minister, who has expressed confidence he would be able to show he acted with "scrupulous fairness" when he sets out his full version of events to the inquiry.

He told MPs this week - amid claims that he was a "cheerleader" for News Corporation's attempt to take full control of BSkyB when he was supposed to be acting "quasi-judicially" - he had requested the earliest possible date to do so.

But a spokesman for the inquiry said: "Lord Justice Leveson is of the view that, in the interests of fairness to all, the inquiry should continue with the existing scheduling of his appearance."

Labour stepped up calls for the Prime Minister to call in his independent adviser on ministerial conduct, Sir Alex Allan.

Deputy leader Harriet Harman said: "It was always the case that it was the responsibility of the Prime Minister and his alone to ensure that his ministers adhered to the Ministerial Code.

"He should never have sought to pass that responsibility off to Lord Justice Leveson.

"David Cameron should now face up to his responsibilities as Prime Minister and refer this matter immediately to the Independent Adviser on Ministers' Interests as he should have done at the outset.

"There is no need for Jeremy Hunt to wait to give his evidence to the Leveson Inquiry and he cannot hide behind it. He should come to the House of Commons as soon as possible."

Hunt announced earlier he was handing over text messages and emails relating to the bid to the Leveson Inquiry into media standards.

He said he was "confident" that the release of his emails and texts would show he handled the BSkyB merger process with "total integrity".

Aides confirmed that the submission would include not only messages sent to Hunt's special adviser Adam Smith, who resigned on Wednesday after the exposure of his contacts with a News Corp lobbyist, but also other communications within his Department for Culture, Media and Sport.