David Cameron is today expected to offer his first explanation of why he has withheld a cache of private emails between himself and Rebekah Brooks from the Leveson Inquiry.

The Prime Minister became embroiled in angry scenes in the House of Commons this week, refusing to tell MPs why he had not disclosed the messages to the judicial inquiry. The email cache, which runs to dozens of exchanges, also includes correspondence with the former News of the World editor and Downing Street communications chief Andy Coulson.

Ms Brooks, the former chief executive of News International, is currently awaiting trial on charges of conspiring to hack phones and perverting the course of justice. She has denied there is any truth in the charges. Mr Coulson is also facing charges of conspiring to hack phones and perjury. He denies any knowledge of phone hacking.

The Independent revealed on Tuesday that the Prime Minister had taken legal advice about not supplying his emails to Lord Justice Leveson.

At the following day's Prime Minister's Questions, an agitated Mr Cameron refused to answer a question on the Brooks emails from a Labour MP. Chris Bryant, Labour's shadow Home Office minister, yesterday tabled five "named day" or written questions that repeated his demand for Mr Cameron to publish "all the texts and emails and other forms of correspondence" between him and Ms Brooks.

The Speaker, John Bercow, considered Mr Cameron's refusal to answer overnight, following PMQs. Yesterday the Speaker confirmed to Mr Bryant in the Commons that his question had to be answered. Mr Bercow said: "Yes. They should be answered; they should be answered on time; and they should be answered substantively. That requirement applies to all members of the Government."

Last night a spokesman for the Prime Minister confirmed Mr Cameron would be responding. Following discussions on the matter involving Mr Bercow, Mr Bryant has been told to expect his written question to receive a written answer from Downing Street.

A spokesman for the Prime Minister said that MPs were free to ask questions which Downing Street in due course was required to answer. The spokesman said: "On Mr Bryant's question, there will be a response in due course." The spokesman declined to say how detailed Mr Cameron's response would be. Under Commons conventions, Mr Cameron has up to three days to deliver his formal reply.

The ruling by the Speaker was not expected in all quarters of the Palace of Westminster. Some MPs had consulted constitutional experts who judged that Mr Cameron was within his rights to refuse Mr Bryant's call to publish, and that it was up to MPs themselves to assess what his refusal meant.

However for those who believed Mr Cameron had broken the conventions set down in the parliamentary bible of practices, Erskine May, there was debate about what sanctions would follow if the PM continued to remain silent on the secret emails. One legal expert in the Commons said: "It would appear Mr Cameron might have to order an inquiry on himself. And no one expects that to happen."

Sources within the Leveson Inquiry have confirmed that the Brooks-Cameron emails were not passed on. Downing Street said only that Mr Cameron had fully complied with the inquiry's demands.

No 10 has since been hit with a series of Freedom of Information requests after effectively confirming the existence of the email cache. Labour's deputy leader, Harriet Harman, has also written to Downing Street urging Mr Cameron to release all the Brooks and Coulson correspondence.

Mr Cameron was advised by lawyers that the Brooks-Coulson emails were not "relevant" to the inquiry into the press, its standards and its relationship with police and politicians.

The contents of the emails are described by sources as containing "embarrassing" exchanges.