Britain's Prime Minister Theresa May speaking in the House of Commons (Photo by HO / PRU / AFP)

THE DUP has said it will not support the British government if it tables a fresh meaningful Brexit vote because "the necessary changes we seek to the backstop have not been secured".

Just hours after British Prime Minister Theresa May announced that she will step down if her EU divorce deal is passed by MPs, Democratic Unionist Party leader Arlene Foster said that her party will not back it.

Ms Foster said that the current withdrawal agreement and Irish backstop pose an "unacceptable threat to the integrity of the UK".

In a statement issued this evening, Ms Foster said that "the backstop if operational has the potential to create an internal trade border within the United Kingdom and would cut us off from our main internal market, being Great Britain.

"We want to secure the United Kingdom's departure from, and our future relationship with, the European Union on terms that accord with our key objectives to ensure the integrity of the United Kingdom."

Mrs May said this evening that she would quit if her twice-defeated EU divorce deal passes at the third attempt, making a last-ditch attempt to persuade rebels in her Conservative party to back her, an MP in her party said.

Mrs May has told Conservative MPs she "will not stand in the way" of the party having new leadership for the second phase of Brexit negotiations, telling the 1922 Committee: "I am prepared to leave this job earlier than I intended in order to do what is right for our country and our party."

Mrs May "will go if deal gets through," said the MP, who spoke on condition of anonymity. "Suggests she goes after a deal."

Another Conservative member said that while May had not given a date, the impression was that she would go "reasonably soon".

Mrs May's announcement is the latest dramatic turn in the United Kingdom's three-year Brexit crisis, but it is still remains uncertain how, when or even if it will leave the European Union.

Labour leader Jeremy Corbyn said Mrs May's offer to step down in exchange for support for her deal showed her Brexit talks were "about party management, not ... the public interest".

"Theresa May's pledge to Tory MPs to stand down if they vote for her deal shows once and for all that her chaotic Brexit negotiations have been about party management, not principles or the public interest," he said on Twitter.

"A change of government can't be a Tory stitch-up, the people must decide."

Many of the Conservative rebels who want a cleaner break from the EU than May's deal would deliver had made it clear that they would only consider supporting her agreement if she gave a firm commitment and date for her resignation.

Mrs May had already promised to step down before the next election, due in 2022. By agreeing to go sooner, she increases the chances of her EU deal passing before the new April 12 deadline.

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The UK government is now expected to bring the deal back to parliament for a third vote on Friday.

Mrs May's deal means Britain will leave the EU single market and customs union as well as EU political bodies.

But it requires some EU rules to apply unless ways can be found in the future to ensure no border is rebuilt between British-ruled Northern Ireland and Ireland.

Many Conservative rebels have objected to this so-called Irish backstop, saying it risks binding Britain to the EU for years. But given the choice between the backstop and no Brexit at all, more should come round.

Some of the party's most influential dissenters had already indicated they would back her deal, agreed after two years of talks with the EU, saying it was the least worst option.

Mrs May's deal was defeated in parliament by 149 votes on March 12 and by 230 votes on January 15.

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While Mrs May was telling her lawmakers of her intention to quit in a parliament committee room, MPs in the main chamber debated eight Brexit options ranging from leaving abruptly with no deal to revoking the divorce papers or holding a new referendum.

Several options on the table would see much closer alignments with the EU than Mrs May has been willing to consider, including staying in the common market or a customs union. They will vote at 7pm on a ballot paper for as many proposals as they wish. Results will be announced after 9pm.

The United Kingdom was originally due to leave the EU on March 29 but last week the EU granted an extension to the divorce date until April 12.

Reuters