Labour leadership ballot papers will be issued by the Electoral Reform Society so unions cannot try to skew the votes of their members, Harriet Harman is to say.

Candidates will also be 'stress tested' at open, televised hustings in areas of the country where the party failed at the election.

Details of the process are due to be set out by acting leader Ms Harman in a speech at Labour's HQ in central London.

Tensions over the future of the party burst into the open over the weekend after Jim Murphy declared he was resigning as Scottish leader and delivered a stinging parting shot at Unite boss Len McCluskey as a political 'kiss of death'.

Mr McCluskey hit back by arguing that the 'arrogance' of Blairites such as Mr Murphy was to blame for the failure on May 7.

He warned the union could consider cutting ties with Labour if the next person in the top job was not the 'voice of ordinary people'.

Meanwhile, shadow health secretary Andy Burnham has been consolidating his position as the front runner, receiving the endorsement of shadow work and pensions secretary Rachel Reeves.

Mr Burnham denied he was the union candidate in an interview yesterday, insisting he was offering 'change' and 'unity'.

He also made an eyecatching bid to outflank David Cameron on Europe by demanding the in-out referendum be brought forward to next year - saying prolonged uncertainty would damage Britain.

Mr Burnham and the other candidates - so far Yvette Cooper, Mary Creagh and Liz Kendall - will take part in a series of televised clashes in front of audiences drawn more widely than Labour members.

Shadow education secretary Tristram Hunt is set to make a decision this week on whether to throw his hat into the ring.

Ms Harman will say the party must ask itself which individual is best equipped to win over the nation.

'Not the politically obsessed public, the people like us, but the people who don't decide about their choice of MP and choice of government until they have to,' she will say.

'We need to see this process as one that is not merely electing a new leader and deputy leader. But one that is helping to rebuild old connections and fashion new connections with a public that rejected us north and south.'

Ms Harman will say the 2010 contest that elected Ed Miliband was too much within 'Labour's comfort zone'.

'We were talking to ourselves. We have to look outwards and stress-test our candidates with the public,' she will say.

'So I want to see party meetings where members bring non-members. Where someone who voted Labour brings along someone who voted Tory or SNP, or didn't vote at all.

'We need robust tough televised hustings which involve the public.'

She will add: 'Last time our hustings were in front of Labour members and were in cities where Labour won. We must have those hustings now in towns and suburbs where Labour lost.

'We have to go back and ask local people from those areas to be brutally honest about what they think of us and what they want from us.'

Pointing out that this election will be done on a one-member-one-vote basis rather than through an electoral college as last time, Ms Harman will promise 'strict rules to ensure there is a level playing field for each one of the candidates'.

'Last time the unions communicated directly with many of their members, sending them ballot papers with accompanying material only mentioning one candidate,' she will say.

'There will be none of that this time. The Electoral Reform Society will send out individual ballot papers to each member of the electorate.

'The winner of this election is not going to be the choice of the unions or any single section or faction of the Labour Party. He or she is going to be choice of the Labour Party.'

A new class of 'registered supporters' who have paid just £3 will also be able to vote.