In a speech to the Conservative Party conference in Manchester, Mr Rees-Mogg said that in the eyes of the public the House was at “the lowest point in modern history”,
He was greeted by cheers and a standing ovation as he walked on stage, but the crowd started murmuring in discontent as he spoke about Mr Bercow.
Mr Rees-Mogg said: “As a parliamentarian, no, listen, listen, because I’m actually going to be nice about him.
“As a parliamentarian, I have been in many ways and remain a great admirer of the Speaker.
“He has helped MPs hold the Government to account and to seek redress of grievance.
“But in my view, he has now flown too close to the sun and I hope that as he comes to his retirement he will not allow the good he has done in his earlier years to be forgotten.
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“But his recent mistakes have to my deepest regret as Leader of the House of Commons damaged the standing of the House in the eyes of the British public to the lowest point in modern history.”
Earlier, during a panel discussion on Brexit, Mr Rees-Mogg dismissed the idea of a government of national unity as being a “Remainer coup”.
He said: “It is not unity at all, it is a Remainer coup, isn’t it?
“It’s to try and frustrate and stop what 17.4 million people voted for.
“And the comeuppance they will get if they defy the electorate will come in the ballot box when we come to a general election.
“So fear nothing that they do, fear nothing of their schemes and strategies, because ultimately we will have a general election and parties that deny democracy get into great trouble when people have the chance to vote.”
Meanwhile, Michael Gove said he believes a no-deal Brexit will cause “some turbulence” and warned that not leaving the EU would damage democracy for longer.
The minister, who is in charge of no-deal preparations, also predicted that no other countries would follow Britain in exiting the bloc, but suggested the EU will look “very different” in the next 10 to 20 years.
Speaking in Manchester, Mr Gove told members: “The level of our preparations has accelerated massively since Boris (Johnson) became Prime Minister.
“Now, of course, we can’t anticipate every risk, we can’t guarantee against some turbulence and that’s why we’d much prefer it to secure a deal with the EU before October 31.”
Brexit Secretary Steve Barclay also questioned how much delays to Brexit have cost the country in opportunities.