Prime Minister Theresa May and the main opposition Labour Party leader Jeremy Corbyn will meet again late Monday afternoon to try and hammer out an agreement on Brexit that they hope U.K. legislators can finally endorse, as the latest polls suggest that Britain's largest two political parties face significant setbacks in this month's European parliamentary elections.
May has repeatedly insisted that she doesn't want the U.K. to participate in the EU vote that begins on May 23rd, but there were few signs ahead of this new round of cross-party negotiations that a breakthrough was imminent.
One long-time May ally, British Foreign Minister Jeremy Hunt, said Monday that talks were entering a "crunch week" as he arrived at a regularly scheduled meeting of European ministers in Brussels.
But he restated the Conservative position that any kind of second public vote to ratify the government's Brexit deal would be a "betrayal" of the previous 2016 referendum on EU membership.
This proposal for a so-called "confirmatory" public vote remains hugely popular among Labour Party supporters and is a significant plank in the negotiating position of several top Labour officials.
The deputy Labour leader Tom Watson told BBC radio early Monday that many of his party's legislators would demand just such a measure in return for their approval — an arithmetical necessity if May's negotiated deal with Brussels is to pass successfully through the UK parliament's lower chamber, known as the House of Commons.
"A confirmatory ballot is not a religious point or a point of ideology," Watson insisted, "it's just how do you get an outcome, how do you sort this out?"
But some political analysts say that weeks of unsuccessful talks between the Conservative and Labour leaderships — known as the "front benches' for where they sit inside the Westminster parliament — and a terrible electoral performance by both parties in recent UK council contests, may mean ordinary lawmakers on both sides of the political spectrum have decided to harden their respective stances on Britain's EU membership.
"The local elections increased the incentive for May and Corbyn to get a deal," Anand Menon, director of the London-based think-tank UK in a Changing Europe, told CNBC Monday.
"But they also increased the incentive for Brexiteers in the Conservatives and Remainers inside the Labour Party to prevent a deal. It really ossified everything."
Before embarking on discussions with her opposite number, May promised that if the negotiations eventually broke down, she would pursue another round of what are called 'indicative' votes. This would mean that parliamentarians would be able to indicate their preferred Brexit outcomes, and any preference that won a majority could form the roadmap for the Prime Minister's next course of action.
A Downing Street spokesperson acknowledged to Westminster-based journalists on Monday that the cross-party talks had been both "serious" and "difficult." But the spokesman insisted that if there was a breakthrough in the negotiations any time soon, then the government would still try to hold a House of Commons vote on the deal - encapsulated in a piece of legislation known as the EU Withdrawal Agreement Bill - before the start of European parliamentary elections next Thursday.
But after the three stinging defeats the legislation has encountered since the start of the year, skepticism remains that these ongoing talks could yield any markedly different result.
Menon noted that agreement between leaders of the two biggest parties was no guarantee of success.
"There is a possibility, albeit a remote one, that the two front benches could find an agreement, but that it doesn't get through parliament."
Meanwhile Simon French, chief economist at Panmure Gordon, told CNBC late last week that investors have become increasingly focused not so much on the political intricacies of the current impasse, but instead on the details and length of a transition period, as well as the possibility of a change in government.
French said market participants — especially those focused on the British currency — are looking simply for a "resolution that could lead to more certainty." The pound has traded within a narrow range against the U.S. dollar for the past week, at roughly $1.30.