British Prime Minister Theresa May will offer MPs a vote on whether to hold a second Brexit referendum in a last-ditch effort to get a deal through parliament.

The Prime Minister set out a 10-point compromise package ahead of what she indicated would be her final attempt to secure approval for a deal which has already been rejected three times by MPs.

She said there was "one last chance" for MPs to deliver on the result of the 2016 referendum and take the UK out of the European Union.

Her "new Brexit deal" was agreed by cabinet only after a stormy two-hour session in Downing Street.

As well as vote on a second referendum, MPs will also be offered a choice over the UK's future customs arrangements after talks with Labour collapsed, in part because of the failure to agree on the issue.

They will choose between the government's existing proposal, which allows the UK to keep an independent trade policy but delivers some of the benefits of a customs union, or a full - but temporary - customs union with the EU which critics warn would leave the UK unable to strike trade deals with countries around the world.

In an appeal to MPs, she said that the "biggest problem with Britain today is its politics" but with the right Brexit deal "we can end this corrosive debate".

Downing Street sources said it had not yet been decided whether MPs would be offered a free vote on whether to require a second referendum to "confirm" the deal.

But Mrs May left little doubt that she would oppose it, warning that delaying the Brexit process for months more - perhaps indefinitely - risked "opening the door to a nightmare future of permanently polarised politics".

In a message to MPs she said: "Reject this deal and leaving the EU with a negotiated deal any time soon will be dead in the water."

Read more: Theresa May's ten-point 'new Brexit deal'

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Mrs May has staked her political future on the deal, with the timetable for her exit from Number 10 due to be decided following the vote on the Withdrawal Agreement Bill.

But her hopes of success suffered early blows, with the Democratic Unionist Party, Tory Brexiteers and Labour all lining up to attack the proposals.

Critics pointed out that there was nothing in the Bill which required the Withdrawal Agreement negotiated with Brussels to be reopened.

DUP Westminster leader Nigel Dodds said: "We will examine the legislation closely when the Bill is finally published but the fundamental flaws of the draft Withdrawal Agreement treaty itself remain unchanged.

"Many of the proposals on the backstop serve as an attempt through domestic law to mitigate a bad deal, whereas the focus should be on getting a better deal.

"The only positive vote in the House of Commons on Brexit was the Brady amendment which called for alternative arrangements to the backstop to be implemented in the treaty and other changes to remove the current threats posed by the backstop," said Mr Dodds.

"That still remains the best way forward to a stable majority in the House of Commons which would deliver Brexit and protect the Union. That is what this or a new prime minister must address.

"We will have to await the publication of the text of the Bill to see what the proposals actually mean but the fact is that the fatal flaws of the draft treaty remain," he added.

Scotland First Minister Nicola Sturgeon tweeted: "The PM is asking MPs to vote for a Bill that takes us out of the EU - in Scotland's case against our will - out of the single market and possibly out of the Customs Union. And with no actual commitment to putting the deal to a second referendum. @theSNP will not do that."

She continued: "In PM's own words, 'if MPs vote against the Bill, they will be voting to stop Brexit.' That is what @theSNP will do because Scotland did not vote for Brexit. #StopBrexit."

The "new deal" aimed at delivering Brexit appears to be acceptable to Ireland, Taoiseach Leo Varadkar said this evening.

"We have always said that if this withdrawal agreement bill doesn't contradict the letter or spirit of the withdrawal agreement, including the Irish backstop, well then it's something that we can accept," Mr Varadkar said on RTÉ's Six One News.

"It hasn't been published yet so we don't have a formal view on it... From what I've heard, it sounds like it is okay and would be acceptable."