After talks with opposition Labour leader Jeremy Corbyn on Tuesday evening, May announced that MPs would vote on legislation to implement the Brexit deal in the week starting 3 June.
"There appears to be little prospect of an agreement with Labour and nearly no prospect of some of your colleagues in the DUP coming on board, So is this a last throw of the dice from the Prime Minister?"
The prime minister's Brexit deal will be "dead" if the withdrawal bill does not pass in the Commons in June, Brexit Secretary Stephen Barclay has said.
May was seeking a "stable majority in Parliament that will ensure the safe passage of the Withdrawal Agreement Bill and the UK's swift exit from the EU", the spokesman said.
Approving the bill, which implements the terms of Britain's departure, does not remove the need for Parliament to separately ratify the thrice-rejected European Union withdrawal deal.
Defeat in the vote would likely spell the end of May's divorce deal and probably her premiership.
Ms Allan, who is a committed Brexiteer, has faced online queries over whether she would be supporting the Brexit Party in the May 23 election.
Mrs May will meet leaders of the 1922 Committee of Tory MPs on Thursday, who have urged her to name a date when she intends to leave Downing Street.
Maria Caulfield, the party's MP for Lewes, said last week she "fundamentally disagreed" with holding the elections and may even vote for a Brexit Party candidate.
But progress has been slow.
May's meeting with Corbyn in her parliamentary office was only the third time they have met since the talks began six weeks ago.
Speaking to Iain Dale, she said: "She's just trying to remain leader of the Conservative Party and hope that something's going to turn up".
Corbyn "set out the shadow cabinet's concerns about the prime minister's ability to deliver on any compromise agreement", a spokesperson said.
"The factual position is if MEPs are elected and (the British) parliament has not approved a withdrawal agreement bill which has achieved royal assent by June 30, they will take their seats", May's spokesman said.
If the bill is introduced in the first week of June it will come seven days after the European Parliament elections - which Education Secretary Damian Hinds has acknowledged could be "difficult" for the Conservatives.
Labour is struggling to maintain its finely balanced position on Brexit, promising to both deliver on the referendum but also to keep Britain close to the EU.
May, who became prime minister in the chaos that followed the 2016 referendum in which Britons voted 52 per cent to 48 per cent to leave the European Union, is under pressure from some of her own MPs to set a date for her departure. It will still contain the "backstop" to prevent a hard border in Northern Ireland, and Labour's demands for a permanent customs union will be ignored.
Opposition among Conservatives and their Northern Irish allies, the Democratic Unionist Party (DUP), is focused on the Irish "backstop" plan.
They argue, such a proposal would mean Northern Ireland being treated differently to the rest of the United Kingdom and remaining in a customs union with the EU indefinitely.
The survey for the Times put the Brexit Party on 34 points, well ahead of Labour on 16, the Liberal Democrats on 15 and the Greens on 11.
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