Britain's parliament on Thursday voted to ask the European Union to delay Brexit until at least June and head off a chaotic end to their 46-year partnership in two weeks.

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 UK is barrelling towards the March 29 Brexit deadline with no approved EU withdrawal agreement and a prime minister who appears to have lost control over her bickering cabinet.

Anxious businesses are pleading for action and US President Donald Trump waded in to pronounce himself "surprised to see how badly it has all gone".

A sense of chaos filled the House of Commons this week as lawmakers held a series of votes on ideas about what they could do next.

MPs have twice rejected the deal struck by Prime Minister Theresa May's with the other 27 EU nations -- in January and on Tuesday.

They voted on Wednesday not to leave without an agreement but still lacked a clear roadmap on the way forward three years after Brexit was launched in a bitterly divisive referendum.

The plan they all finally agreed on -- after turning down four other proposals -- was submitted by May herself: to ask EU leaders to simply push Brexit back.

The motion also supported holding a third vote early next week on May's twice-rejected deal.

A revised tally showed it passing by a 413-202 margin despite the majority of her own party -- and seven of her 28 cabinet members -- voting against.

May had already lost her voice earlier in the week and did not stand up to speak before the chamber after all the voting had wound down for the day.

"Parliament’s rejection of no deal and desire for an extension shows there is still some common sense in Westminster," the influential CBI business lobby tweeted after the vote.

"But without a radically new approach, business fears this is simply a stay of execution."

- Another vote -

A bumpy "no deal" exit on March 29 will still happen if May's strategy is voted down for a third time and the EU 27 fail to approve an extension.

EU leaders have said they would consider any request from London.

But they also want to know how long the extension would be -- and what it would be used for -- before they meet in Brussels in a week's time.

May's plan is to hold a third vote on her agreement with Brussels by Wednesday.

Approval would then see her ask for the delay until June 30 so that the treaty can be ratified.

But she warns that her deal's rejection next week could see Brexit postponed for much longer.

A bigger delay would also see Britain take part in European Parliament elections in May -- bizarrely re-immersing the country in EU politics after Brexit was originally meant to have gone into effect.

- Rethinking Brexit -

EU Council chief Donald Tusk said Thursday that the bloc could approve a long postponement "if the UK finds it necessary to rethink its Brexit strategy and build consensus around it".

He reflected Brussels' long-standing position that a closer relationship is possible if May abandons her opposition to staying in the EU customs union.

May's deal has been blocked chiefly by disagreement over the so-called Irish "backstop" -- a measure to keep trade flowing and avoid friction at the border between Northern Ireland and the Republic of Ireland.

Irish Foreign Minister Simon Coveney mentioned the possibility on Thursday of Brexit being pushed back until the end of 2020.

"It would give a long reflection period for the British political system to look at how they want to approach Brexit again," he said.

- No second referendum? -

Parliament's rejection of a second Brexit referendum reflected a broader debate in UK society about how democratic such a vote would be.

Only 85 MPs voted in favour and 334 voted against.

People's Vote and other pro-EU campaign groups have been organising periodic marches across London in support of a second vote that could potentially undo the first one's results.

One rally in October drew around half a million people and was joined by London Mayor Sadiq Khan.

But the group knew it lacked sufficient support in parliament Thursday and withdrew its formal support of the motion before it came up for a vote.

Labour backs the idea in principle but asked its MPs to abstain.