But how likely is a second vote before the UK leaves the EU on March 29? We take a look, below.
Will there be a second referendum?
Theresa May said on January 21 that a second referendum could threaten the UK's "social cohesion".
The PM made the statement as she unveiled her "plan B" Brexit deal to MPs in the House of Commons.
She said a second referendum would "set a difficult precedent" and that the implications for the country were serious.
On January 29 on MPs backed May's "plan B" deal as long as she tries to renegotiate a better deal amid concerns about the Irish backstop.
But senior figures in Brussels, Berlin, Paris and Dublin warned that the demand only made a No Deal Brexit more likely as the clock ticks down to the UK's scheduled departure from the European Union on March 29.
European Commission president Jean-Claude Juncker described the Agreement reached after 18 months of negotiation last November as "the best and only deal possible".
And he told MEPs in the European Parliament in Brussels: "The debate and votes in the House of Commons do not change that.
"The Withdrawal Agreement will not be renegotiated."
What is Labour's position?
Labour leader Jeremy Corbyn has not ruled out calling for a second referendum in a U-turn after May's "plan B" Brexit deal statement on January 21.
He has repeatedly demanded a general election and not supported a second referendum until Labour MPs openly defied him.
But on January 22, it emerged Corbyn has given his backing to Labour MPs' plan for a second Brexit referendum.
It's claimed Corbyn now wants the Government to give MPs the final say on whether there should be a second vote.
If a majority back a referendum, Parliament in turn could force Theresa May to hold a new vote that could lead to Brexit being reversed, reports the Telegraph.
Corbyn had banned his party MPs from speaking with May about Brexit until she scrapped a No Deal Brexit, but Chuka Umunna and Chris Leslie went to No10 on January 21 for talks.
After MPs rejected May's deal on January 15, Corbyn tabled a vote of no confidence in the PM's Government – if it passed it could have triggered a general election.
However, May narrowly survived the vote by 19 votes.
What are the odds of a second Brexit referendum?
Betfair has put the odds at 10/3 that there will be another Brexit referendum and 1/6 there won't.
Paddy Power has put the odds at 1/6 there will not be another referendum and 10/3 that there will be.
Timeline in the build-up of pressure for a second referendum
- January 2018 The former Ukip leader Nigel Farage said on Channel 5’s The Wright Stuff he was considering calling for a second referendum as a way to kill off the topic once and for all.
- March 2018 Leave. EU was fined £70,000 for failing to declare “at least” £77,380 it had spent on campaigning.
- April 2018 The campaign group People’s Vote was started with Labour MP Chuka Umunna at its head, along with three other members of parliament and the actor Patrick Stewart.
- July 2018 Theresa May's Cabinet agrees her latest Brexit strategy, known as the Chequers Plan.
- July 2018 The Electoral Commission fined the Vote Leave campaign group £61,000 after it said it had broken electoral law by exceeding its spending limit.
- July 2018 Shadow Brexit Secretary Sir Keir Starmer said Labour should back a second vote on EU membership if MPs rejected Theresa May’s final deal with Brussels.
- September 2018 Tony Blair, in an interview with Euronews, said the Government's Brexit proposal was "doomed to fail". He warned May's proposal was "the worst of both worlds and will satisfy nobody."
- September 2018 Former Education Secretary Justine Greening said Chequers Brexit plan was “more unpopular than the poll tax”.
- September 2018 Sadiq Khan called for another EU referendum because he believes the people must be given the chance to reject Brexit.
- September 2018 Leaders of Czech Republic and Malta call on Theresa May to commit to a second referendum at a summit in Salzburg.
- September 2018 Labour leader Jeremy Corbyn says his party is open to the idea of a second referendum and said that his party would be prepared to vote down Theresa May's final deal if it "didn't meet their tests".
- September 2018 Party bosses have hinted they'll back a second referendum – but Jeremy Corbyn's closest ally, John McDonnell, has ruled out keeping Britain in the EU
- October 2018 The People's Vote march in London takes place with around 700,000 demanding a final say on the Brexit deal.
- November 2018 A poll finds that the majority of voters in areas held by Labour seats would support a second referendum.
- November 2018 May's Brexit draft passes Cabinet, only to be met with an unfriendly house, and multiple resignations from ministers and key government officers.
- November 2018 The Prime Minister secures the backing of the EU for the UK's Brexit draft deal at a meeting in Brussels.
- November 2018 EU and UK agree on final leaving deal but it still has to be voted through parliament.
- November 2018 Ex-PM Tony Blair claims Labour is about to back a second referendum
- December 2018 Theresa May's Cabinet allies have been asking MPs if they could back a second Brexit referendum.
- December 2018 Work and Pensions Secretary Amber Rudd became the first Cabinet Minister to suggest there "was an argument" for a People's Vote.
- January 2019 Michael Gove says Leave would win second referendum by an even bigger margin.
- January 2019 May's deal gets rejected by parliament 432 to 202.
- January 2019 May narrowly survives vote of no confidence in her Government by 19 votes.
- January 2019 May says a second referendum could threaten the UK's "social cohesion".
- February 2019 May delivers a speech in Belfast on reaffirming there will be no hard border on the Irish island.
- February 2019 PM loses a vote on her latest Brexit plans by 45 votes as Brexiteers said they wouldn't back her – but she vowed to push ahead with her plans to change the backstop
What have polls indicated?
A poll carried out by YouGov on January 16 revealed that 48 per cent said they would vote Remain if there was a second referendum, 38 per cent say they would leave and 14 per cent would be undecided.
After Parliament rejected May's Withdrawal Agreement, 42 per cent said she should resign, 38 per cent said she should stay as PM and 20 per cent did not know.
The question was put to 1,070 British adults.
How would the vote work?
The SNP have said they would back a so-called People's Vote and a number of Conservative MPs have also backed one.
So there could be a majority in Parliament for it but a second referendum will not happen quickly and the first stage is for there to be an Act of Parliament.
That will require the backing of a majority of MPs and it took seven months before Parliament signed off the previous referendum legislation in 2015.
Last time around there was a four-month period between the then Prime Minister David Cameron announcing the referendum in February 2016, and the vote taking place on 23 June.
But the Electoral Commission has said in future there should be at least a six-month gap to allow enough time to register campaigns and put counting officers in place.
There is also the question of what to do about Article 50.
This could be avoided if the EU agreed to extend the Article 50 deadline – but that would need to be unanimously agreed by all EU member states.
Then there is the question of what to put on the ballot paper.
If there are three questions – for example accept a negotiated Brexit deal; stay in the EU; or leave with no deal – then just 34 per cent could decide the winning option.
When was the first EU referendum?
The first referendum on EU membership took place in 1975.
Two-thirds of voters (67.23 per cent) backed the continued membership of the European Economic Community, which the UK had joined only two years before.
Under Harold Wilson's leadership, the Labour Party was trying to present to the public a different version of EEC membership to get a better deal.
The EEC was integrated into the European Union after it was created in 1993.
In the summer of 2016, Britain voted to leave the EU after 17.4million people backed Leave compared to 16.1million Remain voters.
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