Culture Secretary Jeremy Hunt will appear before Leveson Inquiry within the next two weeks

Leveson asked that MPs wait for the three to give evidence "by the end of May", and that Commons Speaker John Bercow not insist on the publication of fresh documentation before the cabinet minister appears.

Media Guardian points out: “Although Bercow can use a Speaker's order to force disclosure, Leveson said he hoped that there would be ‘sufficient respect’ for the Leveson Inquiry to prevent ‘disruption’ of its work.”

Leveson made his statement yesterday in response to a declaration on Monday by the Speaker who said parliament should be pre-eminent and that any "written documents" supplied by the minister to the inquiry should be shared with the Commons as "a courtesy to the house".

Leveson warned MPs that if the Speaker or the Commons insisted on publishing evidence sent by the culture secretary before he had appeared at the Leveson Inquiry, he might be forced to abandon the questioning of Hunt, Michel and Smith on their roles in News Corporation’s £8 billion bid for BSkyB.

The Labour party has already called for Hunt to resign - branding Michel's emails written to his boss James Murdoch as evidence that the culture secretary was biased toward Rupert Murdoch in relation to the proposed takeover.

Hunt has denied that he was party to any improper briefing of News Corporation, but his special adviser Adam Smith resigned last month. Michel said most of his actual communication was with the special adviser, and Hunt concluded that the "volume and tone" of those contacts were inappropriate.

Leveson has already refused any attempt by No 10 to get Hunt's testimony brought forward and yesterday he said that he will approach the inquiry from a "non-partisan judicial perspective".

He repeated his determination not to be drawn into a political debate about the emails released by James Murdoch as part of his testimony into the inquiry.

The judge said he was approaching the subject in a "neutral" fashion and although his investigations may look at the ministerial code and its efficacy, he would not be making any judgment on the issue.

"I do not intend to consider, let alone adjudicate, on the issue of whether the House has been mislead," he explained.

Leveson says it is appropriate to look at the BSkyB bid, including the emails from Michel, but said that "it is a matter for parliament to decide how far either the secretary of state or anyone else should go," in terms of disclosure.

But he said it was important that evidence was released to the inquiry first as this would mean no core witnesses would testify to the backdrop of a politically partisan debate.

"The inquiry permits the public examination of this material in an independent impartial manner, visible to all as it happens," he declared.