Lord Justice Leveson has confirmed he will be calling Jeremy Hunt's former special adviser Adam Smith and the News International lobbyist Fred Michel to appear before his inquiry at the end of May.

The head of the inquiry into media standards has also delivered an irritated response to MPs, following their calls for Hunt's potential evidence to the Leveson inquiry be presented before the House of Commons as soon as possible. Leveson's statement appears to be a riposte to Commons Speaker John Bercow, who made the assertion to MPs on Monday.

The appearance of Adam Smith could be damaging for Hunt - who has always claimed that improper communications between his office and Michel were the actions of his special adviser and not him.

Smith resigned last month after emails provided by James Murdoch to Leveson suggested that he had offered "illegal" advice to News Corporation during its mounting of a takeover bid for BSkyB.

Labour continues to insist that Hunt broke the ministerial code for failing to supervise his political staff.

As a relatively young former special adviser, Smith won't be used to the kind of cross-examination under oath that appearing before Leveson involves. He can expect to be asked whether Hunt was aware of his communications with Michel and the nature of those exchanges.

He will also be asked to comment on claims made by Rebekah Brooks last Friday before Leveson; the former Chief Executive of News International claimed Hunt's office "sought guidance" from the company at the height of the phone-hacking scandal last July - the event which triggered, among other things, the collapse of Rupert Murdoch's bid for BSkyB.

Hunt is also due to appear before the inquiry at the end of this month, with the spectre of being sacked from government hanging over him, depending on what is revealed during his hearing.

In what amounted to a carefully worded way of saying "back off," to MPs, Leveson warned that attempts by Parliament to see evidence intended for his inquiry could damage the fairness of Jeremy Hunt or Adam Smith's appearances before him.

On Monday the Speaker of the Commons John Bercow told MPs: "The accountability of a minister to this house is not diluted or suspended by a ministers' engagement with inquires or other proceedings. When parliamentary questions to ministers are tabled they should receive substantive and timely responses."

However on Tuesday Lord Leveson suggested any overt political point-scoring of witnesses before they appeared could force him to cancel their visits, if political commentary made it impossible for them to get a fair hearing before him.

He said: "To require that to happen could equally undermine the fairness of the procedure... Again, whatever decisions might be taken for the future, I would hope that sufficient respect for my process will allow it to proceed without interruption and without effectively rendering the Order which I have made entirely academic.

Lord Leveson said: "Over the next month, a large number of politicians are due to give evidence on topics that I have no doubt will engage considerable public interest.

"I hope that allowing the Inquiry to proceed as it plans will not amount to a serious inconvenience either to Parliament or to the political process generally. On the contrary, I hope that the process which I have put in place is well placed to assist both.

"The present problem arises only out of sequencing the evidence and, given the timetable that I have explained, I would hope that the overall period within which the evidence will be heard assuages the concerns which have been expressed."