Labour backbencher Bob Marshal-Andrews has become the first member of his party to back calls for the speaker's resignation.
The pressure for Michael Martin to step down over the arrest of Damian Green has not died down, despite his statement to the House on Wednesday.
Mr Marshall-Andrews said: "We should be allowed to do our principal job, our main job, which is to hold the government to account, relentlessly to hold the government to account.
"And an attack on that job and that office is not an attack on [the MP], it is an attack on the people who they represent."
He continued: "There is no greater attack than raiding the office and removing files at the behest and with the consent of the Speaker. And that is, in a very real sense... an outrage."
"If we go into the trenches in order to try to defend this then it would be seen as part of a lamentable history on civil liberties issues and it would do us terrible damage at this stage."
A committee has been established to look at the circumstances around the arrest but it will not convene again until the police investigation is over.