Tony Blair has told Sky News he now believes there is a 50% chance Brexit will not happen.
The former prime minister revealed he feels "much more upbeat" about the possibility of Britain staying in the EU than he did "a few months ago".
"A year ago I put the chances of changing Brexit at about 25%," he said.
"A few months ago, before Christmas, I would have put it at 40%. I think it's now 50%."
Mr Blair was speaking in Brussels, where he was making the case for urgent pan-European reform to immigration rules that he believes could prompt the UK not to quit the EU.
In his latest Brexit intervention, Mr Blair argued if Britain could persuade Brussels officials that it would be prepared to remain in a reformed EU, then the bloc would carry out the required reforms.
He added: "The anxieties which gave rise to the Brexit vote, which I think centre to a significant degree around issues of immigration, well, Europe's also got a big problem.
"It's a huge issue in Germany, it's a huge issue in France, it's a determining issue in Austria.
"It's a big issue in the Italian election now happening. So all over Europe, this is a big problem.
"So, if Europe is smart about it, then it shouldn't treat the British anxiety just as 'oh that's the Brits being unreasonable'.
"It's a major issue around Europe and there are reforms and changes that Europe could propose that would help the British anxiety about immigration, but also help deal with the European anxiety over immigration."
Before the EU referendum in 2016, David Cameron tried to secure reforms to the bloc that he hoped would prompt a Remain vote from the UK public.
The bloc was unwilling to meet all of Mr Cameron's demands, but Mr Blair believes the situation now is materially changed and the EU would act differently.
He said: "Two big differences between now and two years ago are: one, frankly Brexit has happened and Europe is also anxious about Brexit.
"Secondly, the immigration issues within Europe are manifestly convulsing the whole of European politics.
"And, thirdly, it's obvious that the things we need to do in order to strengthen the problems around immigration are things that command widespread support right across the political spectrum.
"Although I understand why people in Brussels may shrug their shoulders and say 'well the British want to do it, there it is'.
"But, actually, if Europe can offer us a different way through to the future and there are real signs of Britain changing its mind – if that happens – then Europe should be willing to offer us a place in a reforming Europe."
Reacting to Mr Blair's suggestion there is a 50% chance of Brexit not happening, Conservative Leave-supporter Jacob Rees-Mogg told Sky News: "It is an odd approach for someone who believes in democracy to take.
"17.4 million people voted to leave and, at the general election, both main parties promised to implement the result.
"Not to do so now would show contempt for voters."
However, Mr Blair says he is not calling for a unilateral decision to overturn the result of the EU referendum.
He believes politics and people-power will reverse the decision once a vote on a final Brexit deal comes to the House of Commons.
He said: "I think it's very hard to see how the Government wins the vote in the House of Commons because the Government at some point is going to have to resolve the dilemma they keep avoiding.
"Either, to minimise economic damage, stay close to Europe – in which case you will have to abide by Europe's rules but you'll have lost your seat at the decision-making table.
"Or, alternately, because you prioritised getting rid of those rules, you'll be in a situation where you're going to do significant economic damage.
"There is no solution to that dilemma. It's not a dilemma you can negotiate around, you are going to have to choose.
"And once the Government makes that choice, I think they are going to find it very hard to get either of those propositions through the House of Commons.
"Now, my view is the principle thing, if we can't get a deal in Parliament, is to realise we come back to the people to have the final say on the final deal."
Mr Blair was also deeply critical of the ongoing Brexit negotiations.
He added: "Unravelling this is a hellishly complicated business and the problem is that it's not that the negotiators on either side are kind of stupid people.
"It's just that the negotiation itself is more and more intricate than any this country has ever embarked upon.
"I mean, [the negotiation] literally has not budged a single inch forward from this time last year."
Mr Blair was critical too of Jeremy Corbyn's leadership of the Labour Party in relation to Brexit, adding: "If I were leader now, I would be hammering the Tories all the time, not just on the destructive impact of Brexit but the distractive impact of Brexit.
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"I don't want to be talking about Brexit; I'd prefer to be talking about the NHS.
"It's a huge distraction, but unfortunately it's a distraction you have either got to remove or resolve."
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