A Tory MP has tabled a Commons motion of no confidence in the Speaker John Bercow.
But former minister Crispin Blunt's early-day motion (EDM) was tabled in his name only after he failed to find 100 MPs willing to sign it.
Mr Blunt wrote to all MPs asking for support, but said he would not publish the names of backers unless they hit three figures in order not to expose them to "retribution" by the Speaker.
Mr Bercow has infuriated Brexit-backing Tories with decisions including a block on Theresa May repeatedly tabling her Withdrawal Agreement in the hope of whittling down opposition.
EDMs - which are not allocated any time in the parliamentary timetable - are rarely debated or voted on, but are used by MPs as a vehicle to express their views on a particular issue.
The Reigate MP's motion states that is "impossible" for the Commons to sustain the belief in the impartiality of the Speaker which is "indispensable" for its successful operation.
Mr Blunt said that Mr Bercow's decisions on Brexit had been "wholly partial" and helped contribute to "national paralysis" on the issue.
"Whilst I am disappointed there are not yet 100 colleagues prepared to openly side with me, I believe I would be failing to stand up for the integrity of Parliament if I did not formally record my protest against his bias," he said.
Mr Blunt claimed that more than 100 MPs were concerned about Mr Bercow's behaviour, but said that members of the Government do not conventionally sign EDMs.
"Many others continue to fear the consequences of being against a Speaker who has such influence over their Parliamentary life, even if they had 100 supporters," he said.
"Some will only support a motion if it was certain to succeed in removing the Speaker. Given that his partiality is in accord with the Remain majority of the House and many can't sign EDMs, that is an impossible ask."
Mr Blunt was critical of Remain supporters, including Labour's Dame Margaret Beckett, who have been willing to overlook bullying allegations against Mr Bercow because they see it as important to keep him in post while Brexit is being debated.
Read more from Yahoo News UK:
Dame Margaret said last year that Mr Bercow should not be removed, insisting that the importance of the Brexit issue "trumps bad behaviour".
Mr Blunt said: "Controversies around his conduct are certain to continue. This motion will lie open for the rest of this Parliamentary session and if 100 MPs let me know that they are prepared to sign it, I will then add their names to my own.
"This, I hope, may act as some brake on his partiality going forward."
The Speaker's office declined to comment on Mr Blunt's motion.