The battle for the soul of the party saw acting leader Harriet Harman warn that the unions should never again decide who leads Labour, criticising the way defeated leader Ed Miliband beat his brother David in 2010 with union votes.
Her comments came as Len McCluskey, the general secretary of Unite, Labour’s biggest donor, did an about turn on threats to disaffiliate from the party.
But the row also saw one leadership frontrunner, Yvette Cooper, claim that the party needed to be “shaken up” from the “old boys’ club” and veteran Labour MP Frank Field demand that it stops taking money from the unions.
In a major speech yesterday, Ms Harman said the party had asked itself the wrong questions in 2010, deciding “who do we like?” rather than “who does the country like?”
She stressed that the influence of the unions over the decision on leadership had been altered by the move to a “one person, one vote” electoral system.
As he declared his resignation at the weekend with a stinging attack on Mr McCluskey, Scottish Labour leader Jim Murphy said he would bring forward a report on the Scottish party following suit and adopting a one member, one vote system.
Mr McCluskey hit back by arguing that the “arrogance” of Blairites such as Mr Murphy was to blame for the failure in the election.
In response to Mr Murphy’s attack on Mr McCluskey, Ms Harman said: “We have had a bitter defeat, we have had a thumping in Scotland.
“It would be very surprising if some people didn’t, from time to time, express an exasperation and frustration and anger.
“These things will be said but we are going to try and keep cool heads and we are certainly not going to change the process and are going to press on.”
Questioned about the row after her speech at Labour’s headquarters in London, she added: “So far as the structural relationship between the Labour Party and the trade unions is concerned, we have got a big change in how we elect our leader.
“We used to have three blocs in the electoral college – the members of the Labour Party, MPs and the affiliated trade unions. Now it is one person, one vote and everybody only has one vote.”
That was a “major recasting” of the relationship between the unions and Labour, she added.
Meanwhile, Mr McCluskey retreated from threats that Unite, which gave Labour £1 million to fight the election, would break away from the party.
On Sunday, a bullish Mr McCluskey claimed that it was “essential” that the correct leader is chosen and pointed out that there was “huge support” for the SNP among his members. He added: “It’s up to them. If they inject more disillusionment in the party then the pressure will grow from our members to rethink.
“It is certainly already growing in Scotland. We have a rules conference in my union in July and there’s already a number of resolutions from Scotland seeking to release them from the rule that kind of limits us just to the Labour Party.”
But yesterday he backtracked, insisting “We have no plans to disaffiliate from Labour. The party has never been more united.”
He described the future of the party as “exciting”.
He added that everyone now agreed it was time to debate Labour’s future but he believed there was an “exciting opportunity” for Labour to “rise like a phoenix”.
But Mr Field, the Labour MP for Birkenhead and a longterm critic of the union links to Labour, said the party should stop taking money from the trade unions.
The former minister said: “I don’t blame trade unions trying to influence the Labour Party but I think we should be very clear that they are one interest and one interest only.”
He said: “I think we should move to a state where we have no trade union funding whatsoever. That, I think, itself would force the Government to face up – with them drawing large sums of money from donors – to the question about, how do we fund political parties so that we are not tied to particular vested interests?”
Mr Field said the next leader should have a “new conversation with the trade unions”.
“Instead of them appearing to bully us, we should say we have got five things we want you to achieve in this coming parliament,” he said.
Labour should challenge the unions on pushing for the living wage and raising productivity, he said. “We give them a constructive agenda and get away from this agenda which makes them look as though they are bullying the Labour Party.”
Shadow home secretary Yvette Cooper said she would shake up the “old boys’ club” at Westminster if she won the race to replace Mr Miliband. Labour has not had a full-time female leader, although Ms Harman and Dame Margaret Beckett have filled the role on an acting basis. Ms Cooper told ITV’s Lorraine “that’s a glass ceiling that, of course, it’s time for us to smash”.
Ms Cooper’s husband, former shadow chancellor Ed Balls –who ran against Mr Miliband in 2010 – lost his seat at the election but was finding solace in the success of his football club, Norwich City, after the team made it to the Championship play-off final.
Ms Cooper said: “It’s hard and when you’ve worked for something and you’ve worked really hard for it and then it all stops, it is tough, but Ed is really strong and obviously Norwich getting into the play-offs has cheered him up a bit.”