The result will be announced on Saturday at around 11.30am in Westminster.
The contest saw initially saw Corbyn only scrape on to the ballot as about 15 MPs lent him their nominations, despite not supporting him, in order to “widen the debate”. However, his campaign was boosted when he won the support of two of the biggest unions, Unite and Unison, and became the only candidate to vote against the Conservatives’ welfare bill while the others abstained.
His campaign has also been helped by a surge in new members and supporters who paid £3 to take part in the vote, leading to a near-tripling of voter numbers to around 550,000 people.
Labour has been dogged by criticism of its handling of the election, after it struggled to deal with the problem of infiltrators from other parties and fake voters signing up to take part in the election.
All candidates have ruled out mounting a legal challenge to the result but many Labour members and supporters were deeply unhappy on Wednesday night that the party had not sent them ballot papers.
These include longtime Labour members who had repeatedly tried to contact the party about their missing ballot papers over the last few weeks.
Many were also angry that Labour decided to close its leadership telephone helpline with 24 hours of voting remaining. Michael Dugher, Burnham’s campaign manager, described the decision as “unbelievable”.
It is understood some of those who feel disenfranchised are seeking legal advice about the possibility of a class action.
Sources in the campaigns believe it is possible Cooper or Burnham could still win if Corbyn gets less than 40% of first preference votes, although the last YouGov poll suggested the frontrunner could even get more than 50% in the first round.
If Corbyn gets less than half the votes, the second preferences of voters for the candidate in last position – likely to be Kendall – would be split among the other contenders.
At this point, either Cooper or Burnham would be knocked out for being in third place and the second preferences of their supporters distributed. It would then be down to a head-to-head between Corbyn and the remaining candidate.
Corbyn, who is on the left of the party, has been MP for Islington North for three decades and has never held a shadow ministerial role.
He has spent much of his time in parliament championing causes such as the Stop the War Coalition, campaigning against the private finance initiative and supporting efforts for peace in the Middle East.
If elected leader, he has promised to give Labour members a much greater say in the party’s policymaking process, in a move that could sideline MPs. His key proposals include renationalisation of the railways, apologising for Labour’s role in the Iraq war, quantitative easing to fund infrastructure, opposing austerity, opposing bombing Syria, controlling rents and creating a national education service.
Only about 20 of the parliamentary party’s 232 MPs publicly support Corbyn’s aims, including fellow leftwingers John McDonnell, Diane Abbott, Jon Trickett and Clive Lewis.
But despite talk among Labour MPs about the possibility of challenging Corbyn’s election, this threat to his authority appears to have somewhat dissipated. Prominent centre-ground MPs including Chuka Umunna and Tristram Hunt have called for unity and support for the leader if Corbyn wins.
The result of Labour’s London mayoral candidate selection will be announced on Friday in the contest between Abbott, Sadiq Khan, Tessa Jowell, Christian Wolmar, David Lammy and Gareth Thomas.
This article was written by Rowena Mason Political correspondent, for theguardian.com on Thursday 10th September 2015 06.00 Europe/Londonguardian.co.uk © Guardian News and Media Limited 2010