Jeremy Corbyn was accused of half-hearted support for the European Union as he arrived in Scotland to try to win over undecided voters.
The Labour leader's own deputy, Tom Watson, also admitted that 4 in 10 of the party’s supporters did not know it backed staying in the EU.
But one Labour MP suggested that Mr Corbyn preferred it that way.
John Mann, who announced that he was campaigning for Leave, said Mr Corbyn had been “equivocal” in the campaign because he knows so many Labour voters back a Brexit.
Today (Sat) Mr Corbyn will tell voters in Aberdeen: “If you want to remain a part of the EU you need to get out and vote for it."
He will also say there is a “positive, optimistic case for voting to remain in a reformed EU”, as he tries to reach out to the tens of thousands of Scots yet to decide how to vote.
Senior Labour figures have launched a concerted push to persuade wavering supporters to vote Remain.
But the emergence of prominent backbenchers Mr Mann and Dennis Skinner bring to 10 the tally of the Labour MPs supporting Brexit.
And two Labour MPs, pro-Brexit former ministers Frank Field and Kate Hoey, predicted that the party could lose a million votes to Ukip at the next general election because of its stance on the EU and immigration.
Mr Field said Labour should be encouraging its supporters to vote "as they believe is in the best interests of our country", not taking a pro-EU stance which risks driving them into the arms of Ukip.
Ms Hoey suggested that Westminster was "going to get a surprise" about how Labour voters would cast their ballots on June 23.
Critics have accused Mr Corbyn of failing to take a strong lead, because of personal reservations about the organisation.
But others, such as Dudley MP Ian Austin, who backs Remain, suggested he was out of touch with voters who backed Brexit.
In comments seen as a swipe at Mr Corbyn, the MP for Islington North, Mr Austin said: "There's no point people in north London lecturing people in places like Dudley about the benefits of immigration without listening to their real and legitimate concerns about this issue and coming up with fair and reasonable answers to address it."
Shadow energy and climate change minister Clive Lewis, an ally of Mr Corbyn, said: "Clearly among some Labour voters there is a concern on the issue of immigration and some people, based on that, will be voting to Leave."
But he added: "The reason that people are concerned about immigration is partly because of the hysteria some politicians and newspapers are ramping up, are whipping up on this."
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