Britain is to exit the European Union in March next year after months of talks that have again exposed the deep divides in both the country's main parties - the Conservatives are all but at war with each other and Labour is also at odds over how to leave.
Mr McCluskey added: 'Here's one of the problems Labour have, there are significant numbers of traditional Labour supporters who are saying we're going to vote Conservative because we don't trust labour to take us out of the European Union despite the fact that Jeremy has said repeatedly, of course we recognise the result of course we respect the result, we're coming out of the European Union'.
'Let's see what comes out of conference.
Jeremy Corbyn was condemned by a Jewish Labour MP.
"But I'm not calling for a second referendum".
"Because we deserve that right to discuss our children's future and our grandchildren's future".
He said the public had already settled the fundamental question of whether Britain should leave the bloc in 2016.
Even in the North and Midlands, where many Labour constituencies voted Leave in 2016, there was overwhelming support - 86% and 88% respectively - for a second vote.
More than 100 local Labour associations submitted motions to the conference urging a public plebiscite, with a choice between leaving on terms agreed upon by the government or staying in the EU.
And the Financial Times leads on plans by Labour for every large British company to hand over 10% of its equity to workers within a decade.
His intervention was a key moment in the drive to break the far-left Militant group's hold over parts of the party, which ended with the expulsion of figures including Liverpool council's deputy leader Derek Hatton.
A Labour spokesman said: "The point Dawn was making was that like the Thatcher government of the 1980s, this Tory Government has prioritised tax cuts for the rich while cutting services like women's refuges that save lives and keep women safe".
Corbyn has so far tried to avoid the divisive subject, instead sticking to promoting a domestic social agenda that helped him upset the odds at last year's general election and strip May of her parliamentary majority. "I really welcome this announcement from the NEC today, I think it's absolutely essential that we have got a woman somewhere near the top of the party".
'The people have already decided on that, ' he told Pienaar's Politics on BBC Radio 5 Live.
Britain's Labour Party Leader Jeremy Corbyn speaks at a vigil for peace in Yemen during the annual Labour Party Conference in Liverpool, Britain, September 23, 2018.