Jeremy Corbyn has launched an audacious bid to defeat his rivals by pledging pro-business reforms to back entrepreneurs as voting begins in the Labour leadership race.

In a move to broaden his appeal to all parts of the party as ballot papers are distributed, Corbyn will announce a series of measures including tax cuts for small businesses and increased spending on training. This comes as polling of Labour voters confirms that the leftwing candidate has a significant lead. According to Opinium, 37% would vote for Corbyn if they had a vote – up 13 points from a month ago. Of 1,940 surveyed, 29% would back Andy Burnham, down 10 points from July. Yvette Cooper attracts 19% and Liz Kendall 15%.

In further developments during a tumultuous week, it has emerged that:

■ Interim leader Harriet Harman blocked demands by at least three senior figures for an emergency shadow cabinet meeting, where it is understood there would have been calls for the contest to be stopped. She rejected the appeal by the shadow ministers, who had been alarmed by the rush of 160,000 people to sign up to vote on the last day of registration, in what one said was an example of “flashmob politics”.

■ The rules of the contest were quietly changed last week by Labour to ensure that MPs’ voting preferences will not be published after the new leader is announced, in a move some believe is designed to conceal Corbyn’s lack of support in the parliamentary party in the event of him winning. A party spokesman said the change had been made after officials were alerted to an outdated rule left over from the 2010 leadership election.

■ Chuka Umunna and Tristram Hunt have written to MPs on the “soft left and the right” to ask them to join a “Labour for the Common Good” group in the Commons to allow the “moderates” to rebuild.

■ Toby Perkins MP, chair of Liz Kendall’s campaign, revealed that he was backing Burnham for second place and urged others to use their preferences to avoid a Corbyn victory.

■ In an interview with the Observer, Burnham conceded that while it was “possible” for Corbyn to win the 2020 election, the party would have a much better chance with him. In a major speechon Monday, Burnham will make a “very personal appeal” to members to read his manifesto and recognise the lessons of the last election.

Before the launch of his “better business” plan, Corbyn said he would champion entrepreneurs and small businesses. “The current government seems to think ‘pro-business’ means giving a green light to corporate tax avoiders and private monopolies. I will stand up for small businesses, independent entrepreneurs, and the growing number of enterprises that want to cooperate and innovate for the public good.

“My ‘Better Business’ plan will level the playing field between small businesses and their workers who are being made to wait in the queue behind the big corporate welfare lobby the Tories are funded by and obsessed with.”

Policies to be introduced include a small-business rate freeze, rent controls to stop local shops being priced out, an increase in spending on training to create a more skilled workforce, and more resources for digital infrastructure and Revenue & Customs to help them clamp down on tax avoidance.

Speaking to the Observer, Burnham, however, said he did not believe Corbyn’s programme, including renationalisation of the energy markets, was economically credible, and claimed that the contest was much closer than the polls so far suggested. YouGov put Corbyn on 57% of the vote last week.

Burnham said: “I think what has happened this week is that silly season has taken over. We had what I consider to be a rogue poll – I don’t recognise the figures in that poll – combined with late sign-ups.

“People are putting two and two together and making five – the world goes a bit mad and I think it has drifted away from the reality of where this race is up, to to be honest with you. I am upbeat confident – it is all there to be won.

“The appeal I am making for people thinking of voting for Jeremy is: read my manifesto, look at the vision I am setting out.This is a big change in terms of the scale of what Labour has been saying in recent times.

“If Labour comes out of this fighting itself we are going to repeat history – we are going to go back to the early 80s when factions were fighting each other within the labour party and we left the pitch clear for Margaret Thatcher to bulldoze her way through communities.

“It is possible [Corbyn could win the general election]. But I would say without a credible vision on the economy I think it is difficult.”

Separately it emerged that Corbyn wrote in a column for the Morning Star in March that he believed Labour’s 1983 manifesto – dubbed the longest suicide note in history – would be “highly appropriate today to deal with the finance and banking crisis that has been visited upon the poorest people in Britain and, indeed, across Europe”.

In the column, Corbyn added: “The real reason for Labour’s 1983 defeat was the defection of a number of leading figures in the Labour party to the SDP, allowing Thatcher to be re-elected on the same vote as she had achieved in 1979 while calling it a triumph.”