The Foreign Secretary, David Miliband, angered critics of the Iraq war yesterday when he indicated that a long-awaited inquiry into the planning and execution of the conflict, promised by the Prime Minister, would be held behind closed doors.

He told MPs that the inquiry would be approved "as soon as practicable" once most British combat troops had returned home at the end of July. He admitted there were "important lessons to be learnt" from how the campaign was planned and carried out. But Mr Miliband also suggested its proceedings should be held in secret, similar to the Franks inquiry into the Falklands War. He said a private inquiry – proposed by the Conservatives – would prevent leaks, preserve the privacy of troops involved and enable those overseeing the investigation to see confidential Cabinet papers.

"It would preserve confidentiality that's very, very important for all of our troops," he said. "The fact that [Franks] was conducted in private meant it had access to all the relevant papers. Franks was not a judicial inquiry so it did not require its witnesses to have lawyers. There were no leaks or interim findings to distract from the final conclusions and recommendations of the inquiry."

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The Tory motion stating there was "no reasonable impediment" to announcing a Privy Council inquiry (over a judicial one) was rejected 303 to 265, a Government majority of 38.

Mr Miliband's statement came as relatives of some of those killed in the conflict delivered a letter to Downing Street demanding a full public inquiry. A senior government source said a final decision over the type and scope of the inquiry was yet to be made but secret hearings could make the published findings far more comprehensive.

The Liberal Democrats said parts of the inquiry would have to be heard in camera for national security and privacy reasons but holding all proceedings in private would undermine public confidence in the process.

"The Labour Government and Conservative Party must not be allowed to stitch up the British public with the kind of narrow and secretive inquiry which would suit them both," said Ed Davey, the Liberal Democrats' foreign affairs spokesman. "To be effective, this inquiry cannot sit in private and must be as open and transparent as possible.

"We cannot afford another whitewash like the Hutton report if we are to have any hope of restoring British democracy's reputation at home and across the world."

The Labour backbencher Jeremy Corbyn, who opposed the Iraq invasion, said the case for an inquiry had become "overwhelming" and called for it be "more open" than the one envisaged by the Conservatives.

Mr Miliband promised the inquiry would be "comprehensive" and focus on "both the conduct of the war and the conduct of the peace-building afterwards". But he would not confirm whether it would cover the Government's use of intelligence in the run-up to the war, or whether Tony Blair misled Parliament over the threat posed by Saddam Hussein. The Tories accused Mr Miliband of delaying the inquiry so that its potentially damaging findings would not be published before the next general election. Mr Miliband said it would be approved as soon as possible after 31 July, when British forces in Iraq are reduced to a rump of under 400 personnel. But since MPs head home for the summer recess from 22 July, a formal announcement of the inquiry could not be made before October.

The shadow Foreign Secretary, William Hague, said there was no "reasonable impediment" to beginning the inquiry straight away. He called on Mr Miliband to make an announcement before Parliament breaks up for the summer.

"This should have been done long ago," he said. "It is alarming that by setting a date of 31 July, when Parliament will have adjourned for the summer, the Government are now dragging out at the setting up of an inquiry until the autumn. This is unacceptable."