Jeremy Corbyn is set to storm the Labour leadership after a YouGov poll predicted he would finish 32 points ahead of his nearest rival and win the contest after the first round of voting. Support for the left-wing Islington North MP has surged 17 points since July, and the poll predicts momentum is with Corbyn and he would romp to victory with 53% of first-preference votes, enough to prevent the race going to a second round.

Under Labour party rules, if none of the candidates wins 50% or more of the votes straight away, then the last placed candidate is eliminated and their second preferences are reallocated until someone reaches the 50% threshold. The snapshot, which questioned 1,411 eligible Labour voters for The Times newspaper, put Andy Burnham in second place with 21% (-5) of first choice votes, Yvette Cooper at 18% (-2), while Liz Kendall would finish with 8% (-3).

Peter Kellner, political commentator and president of YouGov, said the working class could play a decisive role in the vote. "Only 33% of our sample are working class electors (compared with 43% in the electorate as a whole). This could be too low. If it is, then we might be understating Corbyn's support, as he does slightly better with C2DE members of Labour's electorate than ABC1 members."

Kellner stressed that the results provided a "situation report", rather than a "firm prediction" on the leadership election which will conclude on 12 September when Ed Miliband's successor is announced at a special Labour conference."They have time to change their minds. Could some people who now say they support Corbyn draw back at the moment of decision – or, alternatively, does his bandwagon have further to roll?" Kellner said.

The figures suggest "Corbynmania" is still in full swing despite calls from some of Labour's big beasts to put an end to the leadership tilt. Figures including Tony Blair, Jack Straw and Alan Johnson have attempted anti-Corbyn comments but none appear to have stuck on the candidate, whose policies include renationalising the railways, ending the Trident programme, and anti-austerity measures.

Tom Watson is on course to win the deputy leadership with 40% of the vote, YouGov also predicted, with Stella Creasy finishing in second place. The public has until midday tomorrow to register before voting starts next week. The result will be announced at a special Labour conference on September 12.