But lawmakers also rejected a call to use that time to hold a second Brexit referendum - a blow to the hopes of a large swath of Britons who still dream of keeping their European identities.
The cross-party amendment, tabled by MPs including Labour's Hilary Benn and Yvette Cooper and Tory Sir Oliver Letwin, would have forced a set of "indicative votes" to determine the preferred Brexit outcome of the House of Commons.
They wanted a series of different Brexit options (soft Brexit, hard Brexit etc.) to be put before MPs in what's known as "indicative votes". This means that May must apply for an extension to Article 50, which is the transition plan enacted by any member state that wants to withdraw from the EU.
If May's deal doesn't pass next week, she will ask the European Union for a delay of unspecified length, adding another great big unknown to a process already full of them.
Before the main vote, MPs rejected an amendment calling for a second referendum by an overwhelming 334-85.
The British parliament voted overwhelmingly Thursday to seek a delay to the March 29 exit date enshrined in law. May's spokesman said the government was still making preparations for a no-deal exit.
The legislative defeats have shredded May's authority and obliterated her control of a fractious Conservative minority government. "When the real costs of Brexit are measured up against the broken promises made for it in 2016, we believe Parliament will have better opportunities to decide it is only fair and reasonable to give the public a real say on this crucial decision for our country".
Theresa May said she would allow her lawmakers to vote according to their own beliefs rather than along party lines on Wednesday, meaning members of the cabinet can vote against her and each other without having to leave the government.
It also nixed the idea of a new public referendum on whether to leave the European Union - a "re-vote" of the question that the public narrowly approved in 2016.
Campaigners for a new referendum are divided over whether the time is right to push for a second Brexit vote.
"But I gave the prime minister my ideas on how to negotiate it and I think you would have been successful".
"She didn't listen to that and that's fine - she's got to do what she's got to do".
Leaving the European Union without an agreement, some experts worry, could lead to food shortages and trade-related chaos.
"In addition to uncertainty about what is going to happen, now there's uncertainty about when it will happen", he said.
The council's president, Donald Tusk, has indicated openness to a long extension.
European Council President Donald Tusk tweeted yesterday he will appeal to EU leaders "to be open to a long extension if the United Kingdom finds it necessary to rethink its Brexit strategy and build consensus about it". MPs have already agreed to that to enable all the necessary legislation to be passed.
But there was no immediate sign of any major shift in the views of Conservative hardline eurosceptics who have so far thwarted the prime minister.