MPs voted down all the four Brexit proposals chosen by House Speaker John Bercow in a bid to break the current Brexit deadlock.
The options included remaining in a customs union with the EU - which failed by just three votes - and holding a new referendum on Britain's membership in the bloc.
The political chaos forced May to postpone Britain's exit from the original date of March 29, but she said it would be "unacceptable" for a further delay beyond European Parliament elections on May 23-26.
Three days after the date on which Britain was originally due to leave the European Union, it is still uncertain how, when or even whether the United Kingdom will say goodbye to the bloc it joined 46 years ago.
Rather than the usual procedure of voting with their feet by walking through "aye" and "no" lobbies, members of Parliament each received a paper ballot listing all four options.
Following the vote, the government said the results demonstrated that its plan was the best and hinted that it could be put before parliament once again this week.
"If it is good enough for the Prime Minister to have three chances at her deal then I suggest that possibly the House should have a chance to consider again the options that we had before us today, in a debate on Wednesday, so that the House can succeed where the Prime Minister has failed, in presenting a credible economic relationship with Europe for the future that prevents us crashing out with no deal".
A proposal to hold a confirmatory referendum on any deal got the most votes, but was defeated by 292-280.
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Mrs May was coming under intense pressure from Brexit-backing ministers and MPs to resist any outcome which would see the United Kingdom remain in a customs union, preventing it from striking new trade deals elsewhere in the world. As things stand, Britain will now depart at 2200 GMT on April 12.
Conservatives had been given a free vote, but Cabinet ministers abstained.
Sterling rose 0.8 percent to as high as $1.3135, also finding support from better-than-expected manufacturing survey data and media reports that the opposition Labour party would support closer ties with the European Union in Monday's series of votes on parliament's favoured Brexit option.
A letter to the Prime Minister signed by 170 Tory MPs demanded Britain leave by May 22 at the latest "with or without a deal".
Smith also claimed the result of the 2017 General Election - which saw the Conservatives lose its parliamentary majority - should have alerted colleagues to the fact a softer Brexit was on its way.
Following the result, Guy Verhofstadt, leader of the European Parliament's Brexit committee, said: "A hard Brexit becomes almost inevitable".
He added that MPs would have "one last chance to avoid the abyss on Wednesday".
None of the Monday votes on the proposals are legally binding, meaning it will be up to the British government if they act on the results.