London (CNN) It was only months ago that the mere utterance of a second referendum would be palmed off by the bulk of Britain's political class as wishful thinking by "remoaners" who voted to stay in the European Union.

But as UK Prime Minister Theresa May ended her most tumultuous week since coming into power, and parliament remained gridlocked over her withdrawal agreement, some prominent Conservative party politicians were reportedly arguing that the only way out of this political impasse is to bring the question back to the people.

What was once considered unthinkable is now, according to the Sunday Times, being discussed, with some of May's most senior allies preparing for a second referendum.

Cabinet Office Minister David Lidington, May's de facto deputy, held talks with opposition Labour party lawmakers in a bid to build a cross-party coalition for a second people's vote, the paper reported . He is part of a group of senior ministers -- Philip Hammond, Amber Rudd, David Gauke and Greg Clark -- who believe a new referendum is the only way to break the parliamentary gridlock, it added.

The Sunday Times also reported May's Chief of Staff Gavin Barwell told Cabinet ministers that a second referendum was "the only way forward." Both men later distanced themselves from the report on Sunday, with Barwell taking to Twitter to deny the claims.

Since there is an unusual level of interest this morning in what I am up to, happy to confirm I am off to play football followed by a few hours work (this will *not* include planning for a 2nd referendum) followed by putting a Christmas tree up

May also criticized the report, saying in a statement that "another vote which would do irreparable damage to the integrity our politics, because it would say to millions who trusted in democracy, that our democracy does not deliver."

The Prime Minister's statement came after she hit out on Sunday at her predecessor Tony Blair's own calls for a second referendum. May condemned his call as an "insult to the office he once held and the people he once served." In response, Blair said he was speaking in the national interest and in the interests of democracy.

"Far from being anti-democratic it would be the opposite, as indeed many senior figures in her party from past and present have been saying," he said according to Press Association. "What is irresponsible, however, is to try to steamroller MPs into accepting a deal they genuinely think is a bad one with the threat that if they do not fall into line, the government will have the country crash out without a deal."

But even if May and the opposition leader of the Labour Party Jeremy Corbyn are united in their distaste for a second referendum -- at least publicly -- it is increasingly looking like a viable option.

British bookmaker William Hill estimated the probability of a second referendum at 54%. "We think she (May) is out of options and the most palatable of the two remaining options (which includes revoking Article 50) is a people's vote," spokesperson Rupert Adams told CNN.

Those odds began to shorten for a second plebiscite on Monday, when the European Court of Justice ruled that Britain could cancel Brexit without the permission of the other 27 EU members. That decision came as news filtered out that May would abort a parliamentary vote on a withdrawal agreement she drafted with the EU , after it became clear she would lose the vote "by a significant margin."

The embattled leader then staggered through a vote of no confidence, triggered by hardline Brexiteers. She survived the vote by 200 votes to 117, but what it revealed was one third of her MPs don't support her Brexit plans -- and more than 170 of those who publicly stated they backed her are on the government payroll.

Risk of no deal

Amid this political crisis, which has been called the "greatest failure of British statecraft since Suez," it's unclear how, or if, either side has shifted public opinion.

By Thursday, Brussels had refused to give May concessions to make her package palatable to British lawmakers. Brexit is more deadlocked than ever; and with just over 100 days before the March 29, 2019 deadline to leave, time to find an alternative to her deal is vanishing. What this risks is crashing out of the EU without a deal, which experts agree would be catastrophic for the British economy.

The Bank of England warned in November that such a scenario would sink the UK economy into recession

Leaving with no deal means dropping out of the legal and regulatory frameworks that have governed the UK's trade, and much of its internal economy, for more than 40 years. It could disrupt food and manufacturing supplies, with many British exports losing their accreditation to be sold in the EU. The government has also warned planes could be grounded , with up to six months of disruption at some ports.