The head of Liz Kendall’s campaign has suggested that Labour supporters will give the party’s leadership to Jeremy Corbyn if they vote for Yvette Cooper. In a dramatic intervention less than a week before the result, Toby Perkins said he believed the complexities of the alternative vote (AV) system, under which voters’ second preferences play a decisive role, left it likely that Andy Burnham was the only candidate able to beat Corbyn.

Perkins, the MP for Chesterfield, said his own team’s canvassing, and that of Burnham’s, suggested that so many of the shadow health secretary’s voters had put Corbyn down as a second preference that Cooper could not prevail if she were left in a runoff with the leftwinger. “My analysis was that Andy Burnham would have a better chance of beating Jeremy Corbyn than Yvette Cooper if he was in the last two,” said Perkins. “On that analysis, I gave Andy my second preference, even though I have liked much of what Yvette has been saying.”

Cooper’s team have dismissed Perkins’s claims, suggesting that Burnham’s vote had been disappearing to Corbyn in recent weeks. John Spellar MP, who nominated Cooper, said he believed his candidate was in a strong position to win.

Under the AV system, each voter can rank the candidates from one to four. When the voting is done, the second preferences of candidates with the least first-preference supporters are distributed, candidate by candidate, until someone has 50% of the votes.

Canvassing by Burnham’s camp suggests that more than half of his supporters have Corbyn as their second preference. This would mean that, if Burnham were in third place to Corbyn and Cooper and the preferences of his supporters were distributed between the two, the leftwing candidate would reap the rewards.

Corbyn is expected to pick up the most first preferences, although it is unlikely that there will be enough to take him past 50% without any second preferences taken into account.

According to Burnham’s canvassing data – involving responses from the 80,494 people eligible to vote – the percentage of his voters who have, or will, put Corbyn down as a second preference has risen in recent weeks from 28% to 51%.

Only 30% of Burnham’s second preferences would go to Cooper if he came third, it is claimed. And even with the second preferences of Kendall’s supporters splitting two to one in favour of Cooper, that is unlikely to be enough to beat Corbyn.

Meanwhile Cooper, who was praised for her stance last week on the refugee crisis, will on Sunday call on Labour members to make sure they use their vote, amid claims that under 50% of those eligible had voted after last week’s bank holiday.

Cooper will say: “With just five days of voting left, Labour members have a huge choice ahead of them, a choice that will not only define our party for the next few years, but will define our country for a decade.

“There’s nothing short term about the decision we make now. Get this wrong and there are five-year-olds today that will spend their whole childhoods under a Tory government. As up to hundreds of thousands of people are still to vote, the choice could not be clearer.”

Kendall will use the final speech of her campaign to issue a stark warning on the threat to Britain’s membership of the EU, and an attack on Corbyn for prevaricating on the issue. She will say: “David Cameron is being dragged to the right by backbenchers more concerned with internal political party management than what is in Britain’s national interest.

“Those on the far left, like Jeremy Corbyn, are failing to show leadership either.

“I’m proud to be the most pro-European candidate in this leadership race. Labour cannot equivocate. It’s time for leadership: ‘maybe’ won’t be on the ballot paper.”