Andy Burnham has appealed to a “silent majority” in the Labour party

to reject Jeremy Corbyn, as his supporters said their data shows the gap between him and the leading candidate is much smaller than previous polls suggested.

Burnham’s intervention signals a change in tone since Thursday, when he warned that attacks on Corbyn risked misreading the mood of the party.

As the first ballot papers are sent out to party voters, the shadow health secretary singled out Corbyn’s plans to nationalise the energy sector and abolish student fees as two policies that were unrealistic.

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Speaking to PoliticsHome, Burnham said: “There is a coalition of senior voices in the party – John Prescott, Neil Kinnock, Margaret Beckett – backing me, saying: ‘Think carefully before you vote and don’t make Labour a party of protest that is racked by internal divisions rather than focusing on being a proper opposition and taking on the Tories.’

“These are people who lived through the mid-80s. There’s a silent majority in the party who aren’t on social media, who will listen to what people are saying and those are the people who are receiving their ballot papers now. The risk is that Labour becomes internally focused, as we were in the mid-80s, rather than a united opposition, and that is something that people do have to think about as they open up their ballot paper. Can the party be united behind Jeremy? I think that is very difficult.”

The shadow health secretary’s camp claimed internal campaign data had him much closer to Corbyn than other polls, with him on 31% and Corbyn on 35%. A source in Kendall’s camp also said they believed Burnham is closer to Corbyn than Cooper, according to their data.

Facebook Twitter Pinterest Andy Burnham: I’m the only one who can beat Jeremy Corbyn. Link to video

Fellow candidate Yvette Cooper, the shadow home secretary, delivered the first detailed critique of Corbyn’s positions on Thursday over his plans to bring back coal mines and print money to pay for infrastructure investment.

Liz Kendall, the fourth candidate, also joined the fray by questioning whether his views on the IRA could destabilise Northern Ireland. She later went even further than this by saying the choice of Corbyn would be tantamount to submitting “our resignation letter to the British people as a serious party of government”.

Asked on Thursday about criticisms of Corbyn, such as those from Tony Blair and Cooper, Burnham initially said attacking the Islington MP was misreading the mood of the party “because what people are saying is they’re crying out for something different, they are fed up with the way, particularly Labour, has been conducting politics in recent times”.

But on Friday, he told the BBC that Corbyn had failed to explain how he would pay for his ideas. “Jeremy’s plans lack credibility. It’s not possible to promise free university education, re-nationalising the utilities, without that coming at a great cost and if you can’t explain how that is going to be paid for then I don’t think we’ll win back the trust of voters on the economy,” he said.

“So there is a real choice here. There are two big visions for Labour going forward. Mine has credibility at its heart, and I believe that is essential if Labour is to win the next general election. As ballot papers land, that is the decision that members of the party have to make.

Corbyn’s rivals, who for weeks were relatively restrained in their remarks about him, have become increasingly outspoken about the threat they claim he poses to Labour’s future in the light of fresh polling suggesting he is extending his huge lead in the contest. However, there is some concern among MPs who do not want to see Corbyn elected that excessive warnings risk looking like the other candidates are ganging up on him and that criticism from people associated with the Brown and Blair eras risks backfiring.

Facebook Twitter Pinterest Yvette Cooper speaks out on Jeremy Corbyn’s policies on Thursday

Corbyn is holding a rally on Friday in Glasgow to launch his 10-point Standing to Deliver plan where he has had to book a bigger venue to accommodate all those who want to attend.

It was revealed this week that more than 600,000 people could vote in the contest, because of a last-minute surge in the numbers signing up as registered supporters and trade union affiliates.

It is thought that the surge in the number of people signing up to vote has boosted Corbyn’s chances, because polling suggests people in these groups – registered supporters and trade union affiliates – are even more pro-Corbyn than ordinary party members.

According to the Times, in the light of the new figures and what they say about the composition of the electorate, YouGov has revised the implications of its latest poll, and now estimates that Corbyn is on course to win with 57% of first-preference votes.

In her Today interview, Kendall urged her supporters to use their second and third preferences to try to stop Corbyn winning. But that would have no impact on the result if Corbyn wins on the first ballot, as the YouGov figures suggest he might, because second and third preferences would be irrelevant. Cooper has also asked her supporters to use all their preferences.

On Newsnight on Thursday, Cooper warned of the risks to the party if Corbyn won: “I think there is a serious risk that the party will split, will polarise and I cannot bear to see that happen because there is too much at stake.” Cooper said the contest was a “battle not just for the soul of the party but it is a battle for all the people we should be standing up for”.

However, Kendall told Today on Friday that she did not think the party would split.