Some lawmakers questioned whether the proposed legislation was still needed after May said she planned to seek a further short extension to the Article 50 negotiating period ahead of April 12, when Britain is otherwise due to leave without a deal.
He said: "It's regrettable that what we have been saying for several months now is coming to pass, but that is the remorseless logic of not backing the Prime Minister's deal".
"I recognise my responsibility", Corbyn said, stressing that the most important issue was "to make sure we don't crash out of the European Union next week with no deal".
The result paved the way for MPs to then try and rush through Yvette Cooper's European Union Withdrawal (No 5) Bill, to prevent no deal, in just one day.
Additionally, even after May's decision to share Brexit decision making with the Opposition and to request a further Brexit delay, Brussels sources have suggested that a second extension may not be guaranteed, particularly as when the first extension was granted, European Union leaders said a second would only be agreed if May's Withdrawal Agreement was passed in the Commons by last week.
"We must really take a no-deal into account", Prime Minister Mark Rutte said in Luxembourg after a Benelux summit.
Mrs May said on Tuesday that she would seek an extension beyond next week to allow negotiations with the Labour leader aimed at ensuring the United Kingdom leaves the European Union "in a timely and orderly way".
"They want a solution, the country needs a solution, the country deserves a solution and that's what I'm working to find".More news: Replacing Obamacare is still a Republican duty
Earlier this week the British House of Commons again voted down all the Brexit options. "And we'll ensure that those are on the table", he said.
Using a nickname that plays on May's reputed robotic inflexibility, one Brexit-supporting Conservative lawmaker told Reuters: "The Maybot has gone haywire - we've got to find the "off" switch".
Mr Corbyn said he welcomed Mrs May's "willingness to compromise to resolve the Brexit deadlock", but otherwise avoided the issue during their weekly Commons clash.
If not, she promised to allow MPs to direct what she does, expressing hope that Britain could still leave with a deal before May 22, so it did not have to take part in European Parliament elections.
Theresa May's statement on Tuesday evening represented a significant shift in her Brexit approach, moving away from the prospect of a no-deal split and bringing opposition leader Jeremy Corbyn into the equation.
Speaking to BBC Radio 4's Today programme on Wednesday, Sir Oliver said, "I think he [Corbyn] is somebody that we can do business with".
"You can see there is a situation where there is a Corbyn-led government.at which point the four horses of the apocalypse gallop over the horizon", he said in an interview on Sky news.
The party said Mrs May's lamentable handling of the Brexit negotiations was to blame for her failure to deliver a sensible Brexit deal.