After two years of government squabbling and parliamentary rifts on Brexit, support is growing for the idea that only another referendum can resolve Britains future outside the European Union.

Former education minister Justine Greening on Monday became one of the most high-profile backers of a so-called People's Vote, which is slowly picking up supporters across the political divide.

"The only solution is to take the final Brexit decision out of the hands of deadlocked politicians, away from the backroom deals, and give it back to the people," the Conservative MP wrote in The Times.

She spoke out after Prime Minister Theresa May announced she had finally persuaded her divided cabinet to agree on a plan for future ties with the EU, only for it to collapse spectacularly.

Two top ministers resigned, sparking threats of rebellion among her eurosceptic MPs and raising concerns among some European diplomats that Britain will never be able to agree any deal with the EU.

Former Labour prime minister Tony Blair, a fervent pro-European, repeated his call for a new vote this weekend, saying there was no majority in the House of Commons for May's Brexit plan or any other.

"We are stuck. In any rational world, and I understand that is a big caveat in today's politics, this would go back to the people for resolution," he said.

Reverse Brexit

Former Conservative prime minister John Major, former Liberal Democrat deputy prime minister Nick Clegg and former Labour foreign minister David Miliband also support a second referendum.

They all opposed Brexit, and the main appeal for many supporters of a new vote -- and the reason eurosceptics oppose it -- is the possibility it could reverse the 2016 decision to leave the EU.

This would be technically and politically difficult but some European leaders, notably EU president Donald Tusk, have been making encouraging noises.

Earlier this year, nine pro-European campaign groups moved into shared office space near parliament and in April launched a joint campaign for a People's Vote.

It has coordinated efforts for a public vote in the event that MPs reject the final Brexit deal, which May hopes to agree with the EU by October.

The campaign group proposes two options on the ballot paper -- accepting May's plan, or staying in the bloc.

Blair and Greening suggest a third option of walking away without any agreement at all, which some hardline Brexiteers have advocated.

Shifting opinion

May has repeatedly rejected the idea and her spokesman confirmed this on Monday, saying "under no circumstances" would there be another vote.

The main opposition Labour party, which is deeply divided on Brexit, has refused to rule anything out.

But public opinion is slowly shifting away from Brexit, and in recent months has been moving towards a second referendum.

Even some of those who oppose the idea have begun warning that it might be a possibility as the government veers from one crisis to the next.

Former Conservative leader William Hague warned Brexit hardliners in his party last week it could be an option if they rebel against May's Brexit deal.

"There is a whole range of scenarios in which they get no Brexit, or an indefinitely delayed Brexit, or a change of government or a second referendum," he told BBC radio.

Even Nigel Farage, the founder of the UK Independence Party (UKIP) who helped secure the Brexit vote, mooted the idea earlier this year.

He suggested it would silence the "whinging and whining" of pro-Europeans, before later backtracking.