Ed Miliband will launch a highly personal political fightback when he declares that the Labour infighting of the past week has emboldened him to take radical measures to tackle “zero-zero” Britain in which the poor are forced to work on zero-hours contracts while the rich benefit from zero tax.

In a defiant message to critics within the party, who had hoped to replace him with the former home secretary Alan Johnson, the Labour leader will quote the German philosopher Friedrich Nietzsche to insist that his opponents have strengthened his resolve. Miliband will say in a speech at London University: “There is a saying which goes: what does not kill you makes you stronger.”

The remarks mark a shift from Miliband’s position last week when he rubbished the suggestion that he was facing dissent by declaring: “I don’t accept that this matter arises.”

In a BBC interview Miliband acknowledged that he did face opposition when he warned that disunited parties were always punished by the electorate and said it would “unforgivable” for Labour to turn in on itself.

“It is fair to say that we haven’t had the best couple of weeks,” Miliband said. “Disunited parties are parties that the public worry about and I understand that, that’s why we are going to go forward as a united party.”

The Labour leader added: “We are not going to look inwards as a party because, frankly, it would be unforgivable. It would be unforgivable to the people that we came into politics to represent, that we stand for and that I am determined to fight for.”

Miliband will use his speech to say that he remains determined to press ahead with what he insists is his radical agenda to change the direction of the British economy, after critics abandoned their fight to replace him in the wake of the unequivocal declaration by Johnson that he will never stand for the party leadership.

But the Labour leader will deliver his speech in the wake of his lowest ever poll rating. The Ipsos Mori research for the London Evening Standard showed that only 13% of the public believe he is ready to be prime minister, while Labour at 29% has fallen three points behind the Conservative party, which is on 32%.

He acknowledged the poor polls when he said he accepted he had his work cut out to win over voters. But he told the BBC: “I’m not in the whingeing business. This job is a tough job and it should be a tough job – it’s an audition to be the prime minister of the country.”

In his speech Miliband will say he remains committed to the tough general election fight because he is driven by core personal beliefs – in contrast to David Cameron who appears, he will say, more interested in notching up his name on the prime ministerial board.

“You need resilience in this job,” Miliband will tell his audience. “You need fight. But above all, you need belief in what you are doing. Not belief based on a longing to have a picture on the wall down the stairs of Downing Street, not belief driven by a sense of entitlement that it is somehow Labour’s turn. Instead, belief driven by how we must change the country.”

Miliband will open a new phase in his campaign to champion the “squeezed middle”, who have been suffering from falling living standards as wages were outstripped by prices, when he pledges to challenge Britain’s “zero-zero economy”. The low rate of inflation means that wages slightly outpaced inflation in September for the first time since 2009.

He will say: “People [are] asking why they are on zero-hours contracts while those at the top get away with zero tax. This zero-zero economy is a symptom of a deeply unequal, deeply unfair, deeply unjust country; a country I am determined to change.”

Miliband will also seek to provide some clarity on Labour’s approach to the deficit amid criticism in the shadow cabinet that Ed Balls has left the party’s position uncertain. Some frontbenchers believe Balls is not being clear enough about the speed of the fiscal consolidation that would take place if he became chancellor.

Miliband makes clear that his government would focus on structural reforms rather than spending. He will say: “Change has to be about big reform, not about big spending. Big spending won’t solve the problems of an economy that doesn’t work for working people and we won’t have the money to do it.”

Miliband will also echo the language of Peter Mandelson, who has complained that Labour is in danger of becoming the party of redistribution rather than the party of production.

On Wednesday Alex Salmond and Nigel Farage, the leaders of the two parties that are doing so much to disrupt the traditional order of British politics, both offered to help support a Labour government in a hung parliament. In separate interviews the leaders of the SNP and Ukip said they would be prepared to agree a “confidence and supply” arrangement – voting for the Queen’s speech and budget but remaining outside a coalition – in exchange for support for their main demands. Salmond demanded full devolution to Holyrood of powers to call another independence referendum while Farage, in the New Statesman, called for a commitment to hold an EU membership referendum.

Salmond even suggested the SNP could help champion northern English cities in a hung parliament. In an interview with Newsweek Europe, the outgoing first minister of Scotland hinted that he might return to Westminster at the general election amid an enlarged contingent of SNP MPs. “It’s likely there is a potential route of progress through Westminster, which has not been the usual circumstance before. Who knows, there might be one or two things we can knock off for the good citizens of Liverpool and Newcastle, because they badly need a champion of some sort.”

Grant Shapps, the Tory chairman, said that Miliband’s speech amounts to his tenth relaunch. Shapps said: “Ed Miliband’s tenth relaunch does not cover up his failure to learn the lessons from Labour’s mistakes. He has opposed everything we’ve done to turn our country around, he’s failed to put forward an economic plan to secure Britain’s future, and all he offers is more of the same failed ideas that got us into a mess in the first place – more spending, more borrowing and more taxes. That is why he is simply not up to the job. Voters will view this latest effort with the same lack of enthusiasm that Ed Miliband’s own colleagues view his leadership.”