One option under consideration is allowing MPs to list their Brexit preferences, allowing their second and third choices to be counted if no one option gets an outright majority, the Telegraph reported.
Five separate dates in mind: UK Prime Minister Theresa May.
"MPs are supposed to represent their constituencies, a lot of the MPs that were in Leave constituencies have repeatedly voted against Brexit motions and it is so frustrating that we're still in this position when we should have left on the 29th March".
Britain's opposition Labour Party, on the other hand, will look to nail down in the next few days whether and how far the government is willing to move in talks over a way forward on Brexit, a Labour Party spokesman said on Wednesday after suffering defeat in United Kingdom local election.
She is immune from a leadership contest until December after surviving one past year.
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"The public no longer trust her to run Brexit negotiations", she said.
Britain's main opposition leader Jeremy Corbyn warned frustrated eurosceptic voters on Thursday they were risking a "Donald Trump Brexit" as he launched the Labour Party's campaign for European elections later this month.
The prime minister agreed a Brexit deal with the European Union last November, but MPs had rejected it three times. "If it were an issue about me and the way I vote, we would already have left the European Union".
"We constantly have lively discussions in the National Executive Committee, however I do not think there will be a row", he said.
The veteran Labour leader said the fledgling party founded by anti-EU firebrand Nigel Farage supported leaving the bloc with no deal, which would result in "an economic shock threatening entire industries".
May yesterday reluctantly accepted that Britain will take part in European parliamentary elections on May 23, nearly three years after voting to leave the EU.