In his first public appearance since announcing his decision to step down as Speaker of the House of Commons, he warned the Prime Minister not to ignore legislation brought by MPs by refusing to ask for a delay to Brexit.
Mr Bercow said “creativity” in Parliament would be employed to scupper a no-deal exit.
A new law passed by MPs last week forces the PM to seek a delay on Britain’s exit until 31 January 2020, unless a deal or no-deal exit is approved by MPs by 19 October.
Mr Bercow added that it would be “astonishing” if the Prime Minister disobeyed the law.
“It would be the most terrible example to set to the rest of society,” he said.
“One should no more refuse to request an extension of Article 50 because of what one might regard as the noble end of departing from the EU as soon as possible than one could possibly excuse robbing a bank on the basis that the cash stolen would be donated to a charitable cause immediately afterwards.”
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He added: “If we come close to being there, I would imagine that Parliament would want to cut off such a possibility and do so forcefully.
“If that demands additional procedural creativity in order to come to pass, it is a racing certainty that this will happen and that neither the limitations of the existing rulebook nor the ticking of the clock will stop it doing so.”
Parliament was suspended - or prorogued - in the early hours of Tuesday and is not scheduled to return until 14 October.
Mr Bercow’s comments brought a sharp rebuke from senior Tories.
Leading Brexiteer Bernard Jenkin said: “The office of Speaker has become irretrievably politicised and radicalised.
“It would have been unthinkable 10 or 15 years ago for the Speaker of the House of Commons to launch a personal attack on the prime minister like this.”
Jenkin also called for reform of the office of Speaker and claimed that under Bercow, support for Brexit had been marginalised because it was a minority view among MPs.
He said: “For one individual in now what is a contested, televised very public and controversial position to have so much unregulated, untrammelled power, is something that the House of Commons is going to have to look at.”
Mr Bercow announced earlier this week he will step down as speaker after a decade in the post by the end of October at the latest.
Announcing his decision, he said the role had been “the greatest privilege and honour of my professional life”.