Theresa May struggles to break through Brexit logjam

British Prime Minister Theresa May was on Thursday struggling to keep her European Union (EU) divorce bill alive for another parliamentary vote, a day after she offered to step down if her Conservative Party MPs agreed to back it.

A number of her Tory MPs are believed to have been swayed by that offer but with Northern Ireland's Democratic Unionist Party (DUP) determined against it, May still lacks the crucial numbers that would be needed for her twice-defeated withdrawal agreement to be voted through in the House of Commons.

Then there is also Commons Speaker John Bercow's diktat in the way that the UK government cannot bring back the same proposal for yet another vote unless it is substantially different from the two previous ones on Britain's exit strategy from the EU, defeated twice by an enormous majority earlier this year.

"The motion tabled will comply with the Speaker's ruling but the only way we ensure we leave in good time on May 22 is by approving the Withdrawal Agreement by 11pm on the March 29 which is tomorrow (Friday)," said Commons Leader Andrea Leadsom on Thursday.

After agreeing to an extension to the March 29 Brexit deadline, the EU had offered May 22 as the outer limit for the UK to finalise Brexit if Theresa May's withdrawal agreement is voted through by Parliament by this week. If she fails a third time, the British PM must come up with alternatives by April 12 or risk Britain crashing out of the economic bloc without any deal in place.

There is speculation that MPs might be asked to vote on the withdrawal agreement but not the linked "political declaration" on the future of the UK-EU relationship to be finalised over a transition period, to make Friday's motion substantially different from the twice-defeated motion.

The Opposition Labour Party branded the move to meet the Speaker's ruling as the "blindest of blind Brexits".

Meanwhile, the Commons failed to find a majority for a way forward after voting for eight different options, including revoking Brexit, leaving without a deal, creating a customs union and backing a confirmatory referendum on any deal, on Wednesday.

After several hours of debate, none of the eight options emerged as a front-runner among MPs.

Conservative MP Oliver Letwin, dubbed "Prime Minister for the day" as he oversaw the unprecedented process of "indicative votes", said the lack of a majority for any proposition was "disappointing".

Alongside the unprecedented takeover by MPs of the business of the House, May told a meeting of Conservative MPs that she would not lead the talks with Brussels over the future relationship between the UK and the EU.

She indicated that she would resign as party leader after May 22 the new Brexit date if her deal was passed, but stay on as PM until a new leader is elected.

"I am prepared to leave this job earlier than I intended in order to do what is right for our country and our party," she told the party's 1922 Committee.

It meant she won some support for her plan but is continuing discussions to try and win over the remaining hard Brexiteers as well as crucially the DUP.