The Labour leader’s remarks follow months of considerable pressure – from both pro-EU Labour MPs and members – for the party to unequivocally support a Final Say vote on any Brexit deal.
Calls were also intensified in the wake of last week’s disappointing local election results for the party, with MPs urging the Labour leadership to stop sitting on the fence over the issue of a second referendum.
So far, Mr Corbyn has resisted such pleas, and on Wednesday reiterated Labour’s policy to support the “option” of a public vote if the party is unable to obtain a “sensible” Brexit deal, or general election.
Addressing the issue during his speech in Medway, Kent, Mr Corbyn said: “Over 17 million people voted to leave the European Union. As democratic socialists, we cannot ignore that.
“We voted to trigger Article 50 in 2017 and promised to respect the referendum in our general election manifesto and again at our party conference last year.
“If we can’t get a sensible deal, along the lines of our alternative plan or a general election, Labour backs the option of a public vote.”
But referring to the option, Mr Corbyn later provided a warmer response to the route of a public vote, telling the audience: “I would want that to be seen as a healing process, bringing this whole process to a conclusion.”
“Nothing is easy in this, but, our essential message has to be to bring people together.”
He also appeared downbeat about the prospect of the cross-party talks with the Conservatives – aimed at breaking the Brexit deadlock – reaching a positive conclusion.
He said it was difficult to negotiate with Ms May’s “disintegrating government” as cabinet ministers are concentrating on succeeding the prime minister, rather than working for an agreement.
Despite discussions between Labour and Downing Street being close to entering their seventh week, he continued: “So far in those talks, there has been no big offer, and the red lines remain.”
Elsewhere in his address, Mr Corbyn also attempted to shift focus from Brexit to austerity, insisting that divisions across the country were not between how people voted in the 2016 EU referendum, but “between the many and the few”.
“Whether you’re from Tottenham or Mansfield, Stockwell or Stoke, here in Medway, or Manchester, so many of the problems you face are the same,” he added in the manifesto launch.
“And while the government’s incompetence and divisions over Brexit have created this deadlock, the injustices in our society are deepening. Those injustices aren’t to do with backstops, implementation periods and all that obscure jargon.”
Turning his fire on Nigel Farage and the newly formed Brexit party, Mr Corbyn said the election on 23 May represented an opportunity to “challenge the poison being peddled” by the former Ukip leader.
He continued: “Nigel Farage’s Brexit is a Brexit for conspiracy theorists. For those who see Muslims and migrants or George Soros as the enemy. Only Labour can see off the Farage snake oil in this election.”
Responding to Mr Corbyn’s speech, Tom Brake, the Liberal Democrat Brexit spokesperson, said: “It’s the same old broken record from Jeremy Corbyn. He is throwing all regard for the environment, for jobs and the NHS out of the window with his personal obsession with taking the UK out of the EU.
“It is clear that Jeremy Corbyn has trashed the hopes of Remainers. Like the Tories, Ukip, or the Brexit Party, a vote for Labour at the European elections is a vote for Brexit.”
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