Ed Miliband has pledged to stand up to “powerful vested interests” in the banking and energy sector as prime minister if he wins the general election next May.

In a speech designed to herald a fightback after facing criticism from Labour MPs, Miliband promised to take on those forces as he said that banks and energy companies must be made to work in the public interest.

But the Labour leader declined to endorse a claim by Andy Burnham, the shadow health secretary, that powerful vested interests have been behind the criticisms of him and his poll ratings in the past week. Asked by the Guardian to explain Burnham’s intervention, Miliband said: “As for the business about the last week, I am going to leave that to others.”

But the Labour leader said that he would challenge banks and energy companies as he said: “My vision of the country is about saying wherever they are – powerful vested interests – we need a prime minister who will stand up to them. That is what I have done as leader of the opposition; that is what I would do as prime minister.”

Miliband’s remarks, in a speech at London University’s Senate House, were designed to show that he is still relishing a fight after a series of Labour MPs said he is leading the party to inevitable defeat in next year. The Labour leader tried to show his confidence as he:

• Criticised David Cameron for “running scared” of the television election debates. “If the Tories are really so confident about this choice between me and David Cameron why is David Cameron running scared of TV election debates? Bring those debates. Let’s have those debates about the future of the country and let the British people decide.”

• Warned that the prime minister is now so “toxic” on the European Union that he is in danger of taking Britain out of the EU. Referring to a speech later on Thursday by John Major, in which the former prime minister will warn that Britain could stumble out of the EU, Miliband said: “John Major’s speech is a pretty devastating indictment of David Cameron. You’ve got John Major, who basically believes in Britain remaining in the EU, saying in not very coded terms that the prime minister’s strategy is burning alliances and burning bridges and not helping Britain in Europe.”

• Launched an attack on Nigel Farage “and his gang” who want to privatise the NHS and who believe women should be paid less than men. Miliband said: “The answer is not to return to a more unequal, more unjust past. Mr Farage, you may want to live in that world. But come the general election, I don’t believe the people of Britain will follow.”

But the main focus of Miliband’s speech was an attempt to revitalise his campaign to champion the “squeezed middle” as he pledged to crack down on Britain’s “zero-zero economy”. This describes what he called the epidemic of zero-hours contracts, which would face a crackdown under a Labour government, and the zero taxes paid by the wealthy.

The Labour leader referred to his groundbreaking “predators versus producers” speech to the Labour conference in 2011 when he spoke of how he would encourage responsible business while cracking down on irresponsible ones. Miliband made clear that the irresponsible businesses of today are the banks and energy companies. He said: “This is about how we change Britain. This is about the fact that there are vested interests in this country, like the banks, like the energy companies, and we need to change Britain. That is what my project is about.

“I have shown, since I became leader, a willingness to take on those forces and to make reforms in order to that. I make absolutely no apology for that. I don’t think any forces should be too powerful.

“I think that is what the British want. They want a government that will say to the energy companies you can’t just rip people off, small businesses that want to know that banks will be made to work for them rather than the other way round.

“It is Labour’s campaign on payday lenders that has actually led to some change. We started talking about [it] and nobody else did. I made a speech some years back in 2011 about predators and producers. At the time people said, ‘Is that really so true?’. You don’t find people saying that any more because people recognise that we do need to change the way the country works.”