The row broke out as voting closed yesterday for the leadership, deputy leadership and London mayoral nomination elections.
The new Labour leader will be announced tomorrow, with the polls suggesting that hard- left candidate Jeremy Corbyn is poised to take control.
Yesterday senior MP Jon Cruddas, who nominated Mr Corbyn to “widen the debate”, warned that a victory for him will turn labour into a “Trotskyite tribute act” from the 1980s.
In the closing hours of the contest, concerns were raised that one in five party members in London may have not received ballots.
David Lammy, one of the mayoral candidate hopefuls, warned there would be a “clamour of people” who would be “very, very upset” that they had been unable to vote for the new leader, deputy and candidate for mayor in the UK capital.
Labour organised a last-minute dash to send new ballots out by close of play yesterday to members who had contacted the party by Tuesday but many supporters have complained they have still not had their voting card.
Voting closed at midday but Mr Lammy said it was unclear how many people had been affected and whether it had altered the outcome of the elections.
The Tottenham MP said: “Over the last few days, if you are ringing 150, 200 people over the course of an evening, what they say to me is one in five people were saying in London that they had not received a ballot and that was up to last night.
“So, I suspect now that this is closed there will be a clamour of people very, very upset, that despite being a member or indeed someone who signed up and paid their £3 and hasn’t been excluded because they do not share the values of the Labour party, for a few of those people they have not been able to vote.
“Now, the extent of this across the country needs proper inquiry and proper understanding and whether it has affected the ultimate vote, I do not know.”
But a senior figure told The Scotsman: “This has been the biggest party election in history and there may have been one or two who slipped through the net but pretty well everybody has received a ballot paper.”
The row come after Blairite leadership contender Liz Kendall launched a fresh attack on frontrunner Jeremy Corbyn and made clear that she is likely to become a frequent rebel if the Islington North MP takes the top job.
In her final speech of the three-month contest just 50 minutes before voting closed, Ms Kendall appeared close to tears as she warned that Ed Miliband’s successor faces “huge challenges” to bring the party together after the “tumultuous and divisive” contest.
The Blairite candidate, who has been dubbed “Tory-lite” by some critics, conceded she may have been “too harsh” in the way she had set out her pitch but insisted it “is never too soon to tell the truth”.
Ms Kendall insisted Mr Corbyn would consign them to opposition and again insisted she would not serve in his frontbench team.
“The programme Jeremy Corbyn offers is not new. His policies and politics are the same now as they were in the 1980s - and will end up delivering the same result.”
Ms Kendall insisted she would not “compromise my principles” on a number of areas including Britain’s membership of Nato, the renewal of Trident or membership of the EU.
She said: “I want to be loyal to the Labour Party whenever I can but there are some things that I believe are so important for the future of the country that I will do what my conscience tells me.”
Ms Kendall told the Press Association that if she had appeared emotional during the speech, it was because she cared so much about the party.
“I feel I’m a tough and emotional woman because I care about these issues so much and I believe so passionately in our party and because I think it is our values and principles that are right for the country but we have got a lot of tough work to do it and I will never stop doing that,” she said.
The party’s former policy chief Mr Cruddas warned that Labour could turn into a “Trotskyist tribute act” under Mr Corbyn.
But Mr Corbyn told ITV News that MPs will have to back him if he wins, even though only half of those who nominated him have backed him.