Labour MP Bob Marshall-Andrews called publicly for Commons Speaker Michael Martin to resign, saying he no longer had any confidence in the Speaker.
Mr Martin disclosed on Wednesday that police did not have a warrant to search Mr Green's parliamentary office.
A "consent form" was signed by Serjeant at Arms Jill Pay for the search, but the backbench MP said the Speaker should be held responsible.
Speaking on BBC Radio 4's Any Questions yesterday, he 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.
"This action, in allowing this to happen in the House of Commons, I frankly do not think he can recover from it, or should.
"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.
"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."