London (CNN)Former UK Prime Minister Tony Blair has said he believes the UK should hold a second Brexit referendum to break the political impasse on the issue.
Blair, who was Prime Minister between 1997 and 2007, said he believed there would soon be a majority in the UK Parliament for a new vote.
Blair's intervention came as Prime Minister Theresa May ended a punishing week -- in which she pulled a vote on her Brexit deal from the UK House of Commons and survived a confidence vote brought by her own party -- with a largely fruitless trip to Brussels and little sign that she would ever be able to win parliamentary backing for the deal.
Speaking at a People's Vote event in London, Blair argued that going back to the British people in a second referendum was the proper thing to do now that people better understood what was at stake -- and that this would bring the country the "closure" it craves, rather than disunity.
"What seemed a few months ago unlikely is now I would say above a 50% likelihood. We will go back to the people. Ultimately, this could even make sense to the PM, who could perfectly legitimately say, 'I did my best, my deal was rejected by Parliament, and you the people must give direction that Parliament cannot,'" he said in his address.
Polling indicates that support for a second referendum on the final Brexit deal -- as promoted by the People's Vote campaign -- is growing, Blair said, at the same time as support for the original decision to leave has fallen.
"Given all that has happened, the undemocratic thing is to deny people a final say," he said.
"In a new referendum both sides will be able to make their case in the context of the experience of the Brexit negotiation, and what we have learned through it. Who can seriously argue that we do not know more today than in June 2016?"
On BBC Radio earlier, Blair said he believed a majority of MPs in the UK Parliament would soon support a second vote.
In his speech, Blair also urged European leaders to prepare for the possibility of a second referendum and to show that it understood the concerns of British citizens and wanted them to remain, rather than being "passive spectators" to the Brexit debate.
"We are now entering a new phase of Brexit. Government has lost the initiative. Parliament has taken it. We know the options for Brexit. Parliament will have to decide on one of them. If Parliament can't then it should decide to go back to the people," he said.
Whether and how a "people's vote" could be held, particularly given that the clock is ticking down fast on the UK's March 29, 2019 departure from the European Union, is far from clear.
May has repeatedly ruled out the prospect of a second referendum and the leadership of the opposition Labour Party has been non-committal on the subject.