The MP for Buckingham has been accused by critics of frustrating the entire process despite his "impartial" role as Speaker. If, as expected, lawmakers reject the government's attempt to call an election, he said he would quit on October 31 - the day Britain is now due to leave the EU.
The Conservatives had said they would run against Bercow in the next national election, breaking a convention that the speaker be elected unopposed.
In January, he came under pressure to resign after he was found to have a "Bollocks to Brexit" sticker in his vehicle window.
She told Today: "This is a Parliament in very hard times".
David Jones, a former Brexit minister, told the Daily Telegraph: "He is gaming the system, as he has done for years".
"Throughout my time as speaker, I have sought to increase the relative authority of this legislature - for which I will make absolutely no apology to anyone, anywhere at any time", he said in the House. The man at the centre of more than three years of fiery Brexit debates in Parliament, Mr. Bercow has been a controversial figure - much criticised by supporters of Brexit and praised by its opponents.
Mr Hill added: "Sir Lindsay Hoyle is the odds-on favourite to replace Bercow in the House of Commons, with Harriet Harman and Rosie Winterton both also prominent in the betting".
Mr Bercow has been given short odds to head to the jungle for I'm A Celebrity following his announcement.
Mr Bercow announced on Monday he would stand down as an MP and as the Speaker at the next election or on 31 October, whichever comes first.
In a speech, he said: "At the 2017 election, I promised my wife and children that it would be my last".
"If the house does not so vote, I have concluded that the least disruptive and most democratic course of action would be for me to stand down at the close of business on Thursday, Oct. 31".
While Mr Bercow moves on to a new challenge, Coral has also offered the latest odds on the next Commons Speaker, with a Labour replacement touted.
Conservative MP Andrew Stephenson shouted at the speaker and left the chamber.
Pro-Brexit campaigner Nigel Farage, one of the architects of the decision to leave the European Union, summed up the eurosceptic sentiment in a two-word tweet: "Good Riddance".