Other amendments selected for a vote by speaker John Bercow include Labour's bid to delay Brexit "to provide parliamentary time for this House to find a majority for a different approach" and Labour MP Chris Bryant's plan to stop a third meaningful vote on Mrs May's deal.
In all, MPs voted to rule out the possibility of a no-deal Brexit by 321 to 278.
The Chancellor is said to have pushed.
She said: "Obviously we continue to be working to leave in an orderly fashion with a deal, but we have made funding available". Tariffs would be maintained to protect some industries, including agriculture.
Tory MPs remain split over what should happen next to try and resolve the deadlock in Parliament. With the Brexit deal now dead in the water, and only two weeks to go until the United Kingdom exits the EU, MPs now face two key votes this week.
The decision to drop all checks to avoid friction at the UK's land border with the European Union will be temporary while longer term solutions are negotiated.
Shadow business secretary Rebecca Long-Bailey told the BBC that Parliament would increasingly "set the agenda" if the government was not in control of events.
Mr Corbyn, in his reply, said: "I do have sympathy with the Prime Minister on her voice and I hope it soon recovers, I understand how painful this is".
"The Prime Minister's negotiations have failed". To take no deal off the table, it is not enough to vote against no deal - you have to agree to a deal.
He added the Commons needs to listen to the country, including workers and European Union nationals who are fearful for their futures, saying of Mrs May: "She needs now to show leadership".
He told MPs: 'We either deliver on the result of the referendum, giving people and businesses across the country the certainty they're calling for and move on as a nation, or we enter into a sustained period of uncertainty during which time the government would work with this House to find a way through, but which I fear would do real damage to the public's faith in politics and trust in our democracy'.
A No 10 spokesman said she did not discuss resigning after her latest defeat because her government had recently won a confidence vote in the Commons.
Today's votes saw three amendments debated and then voted on.
Tory Brexiteer Peter Bone (Wellingborough) asked Mrs May to back the Malthouse amendment, which aims for the United Kingdom to leave the European Union without a deal but also secure a transition period until the end of December 2021.
The EU's chief negotiator, Michel Barnier, has said the current impasse "can only be solved in the UK" and MPs must decide what they want rather than what they don't.
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