The vote was seen as a test of how other populist, anti-establishment candidates might perform in elections across Europe next year.
The huge surge in trade union members registering will aid the left-winger's campaign.
The three non-Corbyn campaigns have sent a joint letter alleging that unfair processing of affiliated supporters, drawn from trade unions, brings the integrity of the election into doubt.
The influx of left-wing members has led some to doubt Tessa Jowell's chances.
A first look at this week's magazine.
Tony Blair would never have talked to Conservative voters they way his successors have talked to Corbynites.
Labour failed to get aspiration or to reach people in and only appealed to one section of the electorate, says Jon Cruddas.
There's only one candidate who can beat Jeremy Corbyn and keep Labour together, says Kevin Meagher.
Most supporters will vote in the next week, most are tired of the contest - a last minute shock is unlikely.
Tricky thing, language.
Forget worries about the polls, forget Operation:Icepick, forget everything. Jeremy Corbyn has won the Labour leadership election.
Buy a friend or loved one a subscription to the New Statesman this Christmas, or treat yourself to weekly issues of high-quality and independent journalism.
Our Christmas subscriptions come with a complementary gift bundle worth £92. Browse our New Statesman subscription options here.