Lord Hague, a former Tory leader and Foreign Secretary, accused Mr Bercow of having not just strong feelings but “an irrepressible urge to advertise them”.
Tory MP James Duddridge has tabled a motion of no confidence in Mr Bercow, which other MPs are being urged to sign when they return to Westminster next week.
Simmering resentment erupted into a revolt after the Speaker said he would not want “racist and sexist” Donald Trump addressing Parliament when he visits the UK.
Lord Hague accused John Bercow of 'advertising his emotions'
Mr Bercow was also revealed to have told students he voted Remain in the EU referendum and that “untruths” were told in the Brexit campaign.
Lord Hague has a history of clashing with Mr Bercow.
Just before the 2015 general election, when Leader of the Commons, he and Tory Chief Whip Michael Gove tried to get MPs to change the rules so that the Speaker would be chosen by secret ballot after the election.
John Bercow's best quotes
Wed, February 8, 2017
Outspoken John Bercow, the Speaker of the Commons, has both wise and not so wise words.
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The Conservatives must realise that being sceptical is different from being phobic in what is an interdependent world.
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The former Tory leader has a history of clashing with the Commons Speaker
Lord Hague said that Mr Bercow had “good points” but also “bad” ones – including expressing his own views in a manner which had undermined the impartiality that was so vital to his job.
Meanwhile, it was reported that Mr Bercow secretly canvassed female MPs’ views before declaring that Mr Trump should not address MPs and peers in Parliament’s historic Westminster Hall, as previous world leaders have done.
Lord Hague Mr Bercow expressed his views in a way that undermined the rules of impartiality
Tory MP Sarah Wollaston tweeted angrily that “at no time did he seek my opinion. I let him know my views on Trump/Westminster Hall but also on Twitter”.
Mr Bercow yesterday continued an official visit to Israel, the first to that country by a serving Commons Speaker.
— Sarah Wollaston MP (@sarahwollaston) 13 February 2017