David Lammy 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 English 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 told BBC Radio 4’s World At One: “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.”
It comes after 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 Jon 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.
He said: “MPs are important but they are not the entirety of the Labour Party.”
Mr Miliband’s successor, along with the new deputy leader, will be unveiled at a special conference in London on Saturday.
Mr Corbyn is the bookies’ outright favourite to win - but Labour’s voting system could still throw up a surprise, as if no contender achieves 50% in the first round of counting, second preference votes come into play, which could allow Andy Burnham or Yvette Cooper to take the top job.