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As part of a now-rejected deal with the Labour party, Theresa May seemed to open the door to a second Brexit referendum.

Theresa May made her final big gamble as prime minister on Tuesday, offering Labour a “new deal” that included the possibility of a second EU referendum in what she claimed was “the last chance” to deliver Brexit.

...

The most ambitious part of her offer involved plans to give MPs a vote on whether to hold a second Brexit referendum to approve a final deal. She said she would respect the result.

Why did she do that? What was her gain in proposing such a gamble, and how does it fulfill her will to deliver Brexit?

_{(I'm turning my comment on Jontia's answer into an answer in itself, not because I think Jontia's answer is wrong, but because I think it doesn't fully explain what's going on.)}

Theresa May is dangling the offer of a Parliamentary vote on a second referendum (or 'confirmatory referendum' as some liken it) if Parliament votes through her Withdrawal Agreement Bill when it comes before them.

Many members of Parliament wanted a second referendum to be part of the Withdrawal Agreement Bill, but instead it's being offered as a conditional second vote.

Why? Because Theresa May knows it will not pass as a vote in its own right.

Each time such a consideration has been voted on in Parliament in the past few months, it has been defeated - firstly a number of times as an amendment (14th March, amendment (h) defeated 334-85 for example), and then twice during the "meaningful votes" debacle:

• 27 March 2019, proposition by Margaret Beckett, "Referendum on the Withdrawal Agreement" was defeated 295-268




• 1 April 2019, proposition by Peter Kyle and Phil Wilson, "hold a Confirmatory Public Vote" was defeated 292-280

As Jontia says, it's smoke and mirrors - she is hoping that the prospect of a vote on a second referendum is enough to gain votes to pass the Withdrawal Agreement Bill whilst knowing she is taking a very small gamble on the second referendum vote.

Uncharitably, Theresa May's latest offer is smoke and mirrors rather than any actual change.

The PM's latest plan is to offer votes on a second referendum and a customs union after the Withdrawal bill has been passed. Crucially, she is not including any second referendum as part of the Withdrawal bill itself.

Leader of the Liberal Democrats, Sir Vince Cable, echoed the point, telling Today: "If [Mrs May] said 'we will put forward the Withdrawal Bill subject to a confirmatory referendum'… we would be obliged to support it on that basis, but she is barely saying Parliament can have a vote if it wants to have a referendum.

"[That] is not in her gift, Parliament will do that anyway. What appears to be a concession isn't."

The BBC Article, that the above quote comes from includes statements from Labour re-iterating that these offers basically allow what MPs can do without government support via the amendment process.

It appears this 4th Bill is an attempt to get both sides on board by telling Leavers that the bill doesn't really include a 2nd referendum and telling Remainers that it does.

Because it costs her nothing and concedes nothing, though her party doesn’t seem to realise that. The Bill at its third reading in the Commons would certainly have had an amendment proposed to require a third referendum (not second; the referendum in 2016 was the second one on the subject), which would have been put to a vote. So there’s no way she could not have a vote on a third referendum. A genuine concession would have been to offer to make the referendum an essential part of the Bill rather than an optional add-on, and have a three-line whip requiring Tory MPs to vote in favour.

A second referendum could very easily produce Brexit in the most painless way.

Have a second referendum, binding this time, with two questions:

1. Do you want to leave the EU or remain in the EU?




2. If the majority votes to leave the EU, do you want to leave with May's deal or without a deal?

Do the referendum, count the votes, and then she can do within days whatever the referendum asked for. The next logical step would be say two weeks time for all parties to sort out their leadership, followed by an election.