Speaking on the fringe of the Conservative conference, the exiled Tory MP urged supporters of another public vote not to let up the pressure, arguing victory was “very close”.
“There is probably a majority in the House of Commons now to deliver it, which is fantastic,” Mr Grieve told the Conservatives for a People’s Vote campaign.
The former attorney general conceded the “very big but” was Mr Corbyn recognising he was unlikely to win a snap election and that he should join the push for a referendum instead.
In a direct challenge to the Labour leader, Mr Grieve said: “Is he going to step up to the mark and act as a statesman, and see that this is the burning issue that we need to resolve first?
“Or is he going to follow what I think is a fantasy path of believing that Labour can somehow take power in December and then deliver something that has eluded everybody else previously.”
Mr Corbyn would need to agree to stand aside to allow a less divisive figure to lead a ‘government of national unity’, to deliver the referendum, he said.
Mr Grieve also ridiculed the argument of critics of a second referendum that the anger it would provoke would lead to riots on the campaign trail.
“I’m convinced that, far from people rioting on the streets, people will say actually this is the one way out,” he predicted.
“It’s pretty difficult for people to riot when they are given a choice – and, actually, a choice to have what they want,” he added, suggesting a no-deal Brexit would have to be on the ballot paper.
The comments come after Tom Watson, Labour’s deputy leader, broke ranks to back a referendum ahead of an election – although the revolt helped trigger the attempt by Corbyn allies to topple him.
The Labour leader says he will vote for an election once Boris Johnson has been forced to secure the Article 50 extension needed to prevent a crash-out on 31 October.
However, it is far from certain that the prime minister – if humiliated by that extension – will still propose an early election, potentially putting a referendum back in play.
The next stage of the campaign will see hundreds of thousands of people descend on London on Saturday 19 October, for the fourth major march demanding a fresh referendum.
The ‘Let Us Be Heard’ event will be staged less than two weeks before the current deadline for leaving the EU – and on the day when the Benn Act, to thwart a crash-out, kicks in.
Mr Grieve suggested the alternative of an election, if Brexit is delayed, would probably produce another hung parliament and fail to produce “an answer to our problem”.
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