Nigel Farage's admission he is on the verge of backing a fresh referendum on European Union membership is the first valid point he has made in his life, Remainers said as they challenged "bring it on".
The former Ukip leader suggested a second vote would put an end to "whinging and whining" by opponents of Brexit and "kill it off" for a generation.
But long-time critics said that while he was "speaking sense" over giving voters another say, he should not be confident of winning a second bout.
Although Downing Street has ruled out a fresh vote on EU membership, bookies have cut the odds of a second round in 2019 to 5-1.
Businessman Arron Banks, a close ally of Mr Farage who poured funds into Ukip and one of the Leave campaigns, has also expressed support for a rematch.
He tweeted: "Alas we always knew the Tories couldn't be trusted to deliver Brexit. The cabinet is Solidly Remain & this fight will have to be re run."
However this has been met bullishly by Remainers.
Lord Adonis, one of the biggest critics of the decision to leave the EU, said: "So Nigel Farage wants a referendum on Mrs May's Brexit deal. I agree. Bring it on."
Labour MP Chuka Umunna, a leading supporter of the Open Britain campaign for close ties with the EU, said: "For perhaps the first time in his life, Nigel Farage is making a valid point.
"In a democracy like ours, the British people have every right to keep an open mind about Brexit.
"If the Brexit that is delivered does not match up to the promises of Leave campaigners - with no sign of £350 million extra per week for the NHS but a whopping great divorce bill of £39 billion - then everyone is entitled to ask if this is the right choice for our country."
Lib Dem Brexit spokesman Tom Brake said: "Tony Blair and Nigel Farage aren't two people I'd normally like to be put in a group with, but on this issue they are speaking sense.
"But Farage shouldn't be so confident of winning. People are now far more aware of the costs of Brexit and the fabrications of the Leave campaign."
Lord Malloch Brown, chairman of Best for Britain, which opposes Brexit, said: "A second referendum: my message is clear - bring it on.
"This is something that the country needs. Every day we see the disaster of Brexit as we see its impact on our economy, jobs, communities and our society."
Ukip's leader Henry Bolton has dismissed Farage's suggestions however, saying: "Ukip policy on a second referendum remains unchanged. The party opposes a second referendum.
"To hold such a referendum would be to call into question the decisive importance of the largest democratic exercise ever held by this country and the unambiguous mandate the people gave the Government on that day - the mandate take us out of the European Union.
"Such a second referendum would set a precedent for revisiting any democratic decision made in future; it would undermine the fabric of our democratic principles and would weaken the clarity and effectiveness of democratic decision."
Prime Minister Theresa May has previously insisted a second referendum would be a betrayal of voters and Downing Street said there would be no re-run.
The PM's official spokesman said: "We will not be having a second referendum."