An unrepentant Liz Kendall said Labour had to stop recoiling from the task of winning back Tory voters, as key figures in her leadership campaign asserted their right to criticise rivals Andy Burnham and Yvette Cooper as continuity candidates committed to the same policies that lost the 2015 election.

There have been reports of splits in her camp as some urge her to tone down her calls for change, and recognise the party membership are not in the mood for a shift to the political centre ground.

Labour's Liz Kendall: I'm not a Blairite candidate Read more

One of her campaign aides, John Woodcock, writing in the New Statesman, expressed his concern that the leftwing candidate Jeremy Corbyn was winning strong applause at party hustings for his positions on Trident spending and foreign policy. He said his open criticism of his rivals on policy was legitimate, and could not be contrasted with off-the-record claims that the Kendall team were a “Blairite Taliban”.

The leadership contest has generally been regarded as tepid with some senior figures in the campaign admitting the contest has driven candidates to focus narrowly on winning votes from the party membership rather than addressing the long-term issues facing the party.

Overall there does not appear to be a thirst in the membership to return to the centre in order to win the next election, but instead to blame specific failings, such as the quality of Ed Miliband’s leadership.

Much of the debate about the party’s future is occurring independently of the leadership contest.

Writing anonymously on the Fabian Society’s website, senior policy advisers in the party urged the candidates to recognise that the deficit is the starting point for a new politics for Labour. “For Labour to win again, a commitment to fiscal responsibility must be defining, not an added extra. Labour should be economically radical because of, rather than in spite of, its commitment to fiscal responsibility. This is the only way social democratic objectives are realised in 21st century.

“If we believe that increased public spending should stabilise the economy during recessions, this also demands a robust acceptance of surpluses in recoveries, subject to the state of investment and public services, which in turn requires reform of the state.”

Interviewed in the magazine Progress alongside the three other candidates, Kendall agreed, saying that everything starts with strong public finances: “We should balance the books and live within our means and get the debt down. Because, unless we do that, we won’t be able to invest in the schools and the hospitals people need. I think it’s wrong to be spending more on servicing our debt than educating our children. Sound public finances and people trusting you with their money and their taxes is the basic test of competence of any party that wants to be fit to govern.”

Facebook Twitter Pinterest Andy Burnham speaks as fellow contenders Jeremy Corbyn, Yvette Cooper and Liz Kendall listen on Sunday. Photograph: Joe Giddens/PA

She adds Labour sometimes appears to recoil from the task of switching voters from David Cameron’s party. “I think I’ll change that because I grew up in Watford, an area which has been Labour, and was a marginal, and now has a stonking Tory majority. And my parents, and my friends and my family, many of whom still live there, want the same things as people who live in a Labour seat like Leicester.

“They want a good job that pays a decent wage; they want to live in a nice home that’s safe for their kids; they want great schools so that their children get the best shot at life; and they want to know that when they retire that they’ve actually got something to look forward to. What people in Watford want and what people in Leicester want, I believe, is the same.”

In the same magazine, Burnham warns the party needs to rethink its approach to public service reform saying, “We got into difficulties in the past where people have not been clear about what the purpose of the reform is. When we were talking about choice ... rightly, people felt there was a hidden agenda around competition and markets and then you get a distrust of the reform ... Or take the health reforms, where Andrew Lansley was saying it was about letting the GP decide. Well, those reforms weren’t about that and that’s what builds distrust between politicians and public services.”

Burnham also praised business people, saying: “Many of them are thoroughly decent people, who work hard to look after their workforce, who probably worry every night when they go to bed about how they are going to make it all add up and ensure that things can be held together.”

In a rejection of Ed Miliband’s 2011 party conference speech, Burnham concludes: “We can’t give out the impression that we see business as predators.”

Cooper argued: “We did well in the cities not the towns. We didn’t do well enough on older voters.” She cautions that this is “not about shifting to the right or to the left. It’s about growing in all directions so ... we carry on talking about the problems with exploitative zero-hours contracts, but we also talk about growing good-quality jobs for the future and working with businesses to do so.

“The debate across the party is about saying: ‘What do you think Labour values are?’ And part of it is about saying: ‘Here are some of the things that the Tories say and do we agree with them or don’t we?’”

Corbyn suggested the party needs to legislate for turning the living wage into a minimum wage set at £7.85 per hour, and 21% higher than the national minimum wage of £6.50 per hour. He argued: “If we say the minimum wage is not a living wage, then what are we saying about the minimum wage?”

He also rejected Burnham’s concern about English not being spoken in the workplace leading to a sense of rejection amongst British workers. Corbyn said: “I thought it was a slightly odd thing to say, and I think we have to stand up for a multicultural, multilingual society. I don’t pretend it’s easy, it’s not ... but if we start conceding that speaking different languages is not acceptable, I think that’s a very, very bad message and if we say, as Ukip do, they would like to reduce the number of foreign workers in Britain, then what happens to the several million British people working all over Europe?”