Speaking at the event in Stevenage on Saturday, the two most established figures in the race described the free schools programme as “a waste of money”.
Cooper told an audience, in which many of the questioners were teachers, that value for money should be the guide in education spending.
“I would rather we were investing money into lower class sizes than new free schools because I think it is a waste of money and bad value for money,” said Cooper.
The shadow health secretary, Andy Burnham, still the bookmakers’ favourite in the race, was swift in joining Cooper in condemning Kendall’s position, which has proved to be an early marker in her quest to be seen as the modernising candidate.
Burnham, who was briefly shadow education secretary under Ed Miliband before being switched to the health brief, said: “We have to bring class sizes down, but the way to do it is not, as some have argued, to support the government’s free school programme.
“As shadow education secretary, I took that decision immediately. How can it be right to be spending money, where there are already surplus places, and taking money away from constituencies where kids are in falling-down buildings in classes of over 30. That can’t be right.
“This whole programme under this government is an experiment with kids’ education and I stand against that.”
Kendall was also heckled by the audience when she stressed her support for Trident, another striking moment in an otherwise relatively low-key event.
Both Burnham and Cooper – although not the leftwing candidate Jeremy Corbyn – spelled out similar positions on unilateral disarmament but were clapped by the audience.
Kendall responded to a heckle by insisting that she would continue to speak her mind. “‘Shame’ some people say, and there will be big differences in our party... Some of you won’t like it, but I have got to tell you like it is,” she said.
A source in Kendall’s camp said: “If Andy and Yvette want to go into the next election with a pledge to close around 900 schools, many of them very popular with parents and pupils, and in marginal seats, then they should make that clear.”
The candidates for deputy leader - Tom Watson, Caroline Flint, Stella Creasy, Angela Eagle and Ben Bradshaw – were also able to present their pitch the to the members at the first public hustings for that role.
Flint, the shadow energy secretary, who tripled her majority in May, gave arguably the most powerful personal statement in which he spoke of her own background.
She told the audience: “My mother had me as a lone parent at 17, I have never known my real dad, we never owned a home, when my mum married in our first flat I shared a bedroom with my sister and my parents.
“Twice in my teens I lived away from home. The second time due to my mum’s alcoholism – an illness that would kill her.
“University was not my destiny, it was an escape. By my mid-20s I had two children under two on my own. I know what it is life to need a Labour government.”
Creasy cited her successful campaign to wake up the chancellor George Osborne to the need for action against high interest loan sharks on the high street and said she wanted to make Labour “a movement not a machine”.
Watson, the bookies favourite who gained the most nominations among Labour MPs to put him on the shortlist for the position, said he was the right person to be in the “engine room” ensuring Labour delivered the vision of its new leader, whoever he or she might be.
Bradshaw stressed his success at the last general election in tripling his majority in what was once a safe Tory seat in Exeter and pointed out the need to win back those who had voted Conservative.
Eagle said that while David Cameron had once told her to “calm down” she would never do so as long as the Tories were in power. She promised to a loyal deputy leader whose advice to the leader would not be given “on the front page of a newspaper”.
This article was written by Daniel Boffey, for theguardian.com on Saturday 20th June 2015 15.07 Europe/Londonguardian.co.uk © Guardian News and Media Limited 2010