"It is highly likely and expected that the European Council will require a clear objective for any extension not least to determine it's length and the European Council has to approve an extension by unanimity".
One of the government's senior law officers, Solicitor General Robert Buckland, said: "We're in a major constitutional crisis here".
Her foreign minister, Heiko Maas, said: "If more time is needed, it's always better to do another round than a no-deal Brexit".
Bercow insists that bringing the same deal, or substantially the same deal, back to the Commons would not be "proper".
"What the government can not legitimately do is to resubmit to the House the same proposition or substantially the same proposition as that of last week which was rejected by 149 votes".
In order to avoid a further stalling of the withdrawal agreement, the British government may now have to come back with essentially the same deal but tweaked with additional side agreements with the EU.
Negotiations with the Democratic Unionist party (DUP) have continued since the weekend, in the hope that if they signal support for her approach, key Brexiters including Jacob Rees-Mogg, could swing their weight behind it.
"May I say how delighted I am that you have made a decision to follow precedent, which is something I am greatly in favor of", said Jacob Rees-Mogg, chairman of the European Research Group of eurosceptics in parliament.
"It is for the British Government and Parliament to decide very quickly what the United Kingdom wants to do next".
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Bercow's pronouncement appeared to take May's Downing Street office by surprise. Downing Street was unable to be more specific on when the plans would emerge.
It comes as German Chancellor Angela Merkel said she will fight for an orderly Brexit right up until Britain's planned departure from the EU. European Union officials say a long delay is probably needed to allow for a total rethink of policy.
He accepted that there would now have to be a "short extension" to the Article 50 withdrawal process as the Government would not be able to get through all the legislation it needed in time for March 29 when the United Kingdom is due to leave.
Explaining that Mrs May "won't be asking for a long extension" when she writes to the EU, Number 10 said: "There is a case for giving Parliament a bit more time to agree a way forward, but the people of this country have been waiting almost three years now".
"Fundamentally, for something to be different, it has to be by definition, fundamentally different".
Brussels and European leaders had made it clear to Prime Minister May after she lost her second vote on the Withdrawal Agreement that the United Kingdom should prepare to make a clean break on the planned departure date of March 29th.
Brexit Secretary Stephen Barclay said that despite Bercow's ruling, the deal could be voted on again if "the circumstances have changed".
However the spokesman said: "She has said in the House of Commons that she does not want there to be a long delay and that she believes asking the British public to take part in European elections three years after they voted to leave the EU would represent a failure by politicians".
After two-and-a-half years of negotiations with the European Union, the outcome remains uncertain - with options including a long postponement, exiting with May's deal, a economically disruptive exit without a deal, or even another European Union membership referendum.