Shadow immigration minister Damian Green reacted angrily today after the Speaker rejected his call for a Commons committee to examine material seized from him by police and decide what is privileged.
Mr Green told the Press Association that Mr Martin had declined his request that the Standards and Privileges committee look at the material seized from his office as part of a Home Office leaks inquiry, which sparked outrage in November.
"Instead, the Clerk to the House has expressed his view about what is covered by privilege, and the police are proceeding on that basis, with no member, and no committee of this house having any say," he said in a statement.
"The Assistant Counsel to the Speaker wrote to my solicitor on January 15 saying that "if there is any continuing dispute over the status of the documents, following the Clerk's consideration of them, it will be a matter for the House to determine at the request of your client Mr Green."
"I have made that request. It has been refused. Why is it that the House's legal advisers can give a clear indication of what should happen, which is then ignored by the Speaker and the Clerk.
"Surely it is for this House to make decisions about matters like this, and not a single official of the House, who appears to be entirely unaccountable and above scrutiny."
Mr Green, whose arrest over Home Office leaks caused a furore, tried to raise the issue as a point of order in the Commons but was cut short by Deputy Speaker Sylvia Heal.
Earlier, in a statement to MPs, Mr Martin said a police request for information on emails between Mr Green and former shadow home secretary David Davis was made to establish their "relevance" to the leak inquiry.
Mr Davis had asked the Speaker, earlier this week, to rule if the request for emails came under his earlier ruling that access to an MP's office or parliamentary papers would not be allowed without a warrant and his personal approval.
Mr Martin told MPs: "I can now inform the House that the request was made by the solicitors for the Metropolitan Police Service to the solicitors acting for the honourable Member for Ashford (Mr Green).
"The request concerned the methods to be used to establish the relevance to a criminal investigation of material which was already in the possession of the police.
"The request did not seek any further material from the honourable Member for Ashford and no approach was made either by the Metropolitan Police Service or the solicitors to the right honourable Member for Haltemprice and Howden."
Mr Green reacted furiously in the chamber later, complaining that Commons officials did not approach him to establish the facts but used the police's "version" of events instead.
"I find it extraordinary that in a matter which concerns emails between two Members of this House, and the fact that they may be private, the House authorities didn't approach me to establish facts, but have approached the Metropolitan Police and have taken as the basis for a Speaker's statement, the police's own version of events - and only their version."
Mr Green raised the issue of Mr Martin refusing his request to refer the issue of parliamentary privilege regarding the seized material to the Standards and Privileges committee.
But he was cut short by Mrs Heal, who told him: "You are an experienced Member of this House and know it is not the appropriate way to question the statement of the Speaker.
"I will ensure the remarks you have made are brought to Mr Speaker's attention."
Mr Davis, in another point of order, said the Speaker had failed to respond to his request that he rule on whether approaches relating to other MPs' communications should come within the protocol published by him in the previous week.
Shadow justice secretary Dominic Grieve said the police appeared to have been making contact "with the House and its servants" to ascertain what might be privileged and what might not.
"As this is a decision which ultimately falls to this House isn't it a strange state of affairs that the House is being denied the opportunity of getting the advice which it needs to make a reasonable decision because there has been no reference to the standards and privileges committee, which has been set up for that express purpose."