The maximum university fee for students will be slashed by a third to £6,000 a year under a Labour government, Ed Miliband has announced.

The policy, revealed by the Labour leader in an interview with the Observer, would be paid for by reversing planned tax cuts for the banks and by asking the highest-earning graduates to pay more interest on their loans.

The move – one of the biggest policy decisions by Miliband in his first year as leader – is designed to appeal to millions of student voters who turned to the Lib Dems at the last election, and to parents worried about the financial burdens of sending their children to university.

Speaking ahead of Labour's annual conference, which opens in Liverpool on Sunday amid rumblings about the party's credibility on the economy, Miliband insisted the plan was "fully costed". He said David Cameron and Nick Clegg would kill off the spirit of ambition and enterprise in the next generation by "loading the costs of paying off the deficit onto our young people".

The unveiling of the new policy comes as the Labour leader's brother, David, prepares to send a message of support to his brother, whose leadership has been criticised in some circles. The former foreign secretary will use a fringe meeting on Sunday, exactly one year after his traumatic defeat in last year's leadership election, to publicly back his sibling: "We must never lose our sense of outrage at this shocking government. Ed has led the party with strong purpose and conviction, and that is what Labour needs."

The Labour leader, who had previously favoured a graduate tax over a fees system, said the cut would mean a wider cross-section of young people going to university, and that it would therefore help create a more equal society. "We can't build a successful economy if our young people come out of university burdened down by £50,000 of debt," he said. "We can't build a successful economy if the kids from all backgrounds are put off going to university."

In contrast to the Tory-Lib Dem coalition, Miliband said he wanted to "invest in our young people by using the talents of everyone, not engaging in tax cuts for financial services."

Miliband's aides said that, if there were an election now and Labour won, it would implement the policy as soon as possible. But they stopped short of promising that the details would feature in three and a half years' time in a party election manifesto. "This is what we would do now. But in three and a half years' time we might be able to do even more," an official said.

From September next year, universities will be able to raise their fees from the current maximum of £3,375 to £9,000, following cuts of 80% in their grants from central government. The controversial decision sparked huge student protests when it was announced last November.

Although ministers predicted that few universities would charge the full £9,000, recent figures show that more than a third – 47 out of 123 universities – will demand the maximum. And whereas the government forecast last year that the average fee would be around £7,500, the actual average will be £8,393.

The money for Labour's policy will come from reversing a corporation tax cut for banks pre-announced by the chancellor, George Osborne, in March – from 28% in 2010-11 to 23% in 2014-15 – and by asking graduates earning over £65,000 a year to pay higher interest rates on their loans.

A debate over Labour's wider economic policy is bound to dominate the conference agenda. While some leading figures in the party are calling on Miliband to apologise more clearly for Labour's economic failings in government and to be clearer about what cuts it would make now, Miliband is standing firm. He insisted he would stick to his central message that the coalition is cutting too far and too fast, without providing more detail of where Labour would withhold funding. "We have got to break this government's addiction to austerity because it is not working," he said.

With competing factions in the party battling to impose their agenda on the leader, former home secretary David Blunkett tells the Observer that Miliband has struggled so far to get his voice heard in the country, urging him to relegate the community politics of "Blue Labour" and focus on defending the previous government's economic record, while providing solutions to the key issues that matter to families.

He said: "There is no question in my mind that the general election will be about how people feel about the future – that's about insecurity, the austerity programme, what is happening about their jobs, their family. We have got to build our confidence and fight back on the central economic difficulties, so we are not defined as being responsible for the deficit that we are facing at the moment."

While Miliband said his determination to sting the banks to pay for a drop in tuition fees showed he wanted the wealthiest to be more responsible, he emphasised that the same community obligations should apply to those claiming benefits. He said he backed ideas floated recently by Liam Byrne, the shadow work and pensions secretary, who suggested that people who were "doing the right thing, getting a job, paying taxes, being good tenants and neighbours and so on" could be placed at the head of the queue for social housing.

After speaking at the Movement For Change fringe meeting, David Miliband will fly to Washington for a conference on China. He will therefore miss his brother's speech on Tuesday.

Today, in a letter to this newspaper, leading Labour figures, including former home secretary Alan Johnson and ex-deputy leader John Prescott, back the creation of a fund to ensure more people from low-income groups can become parliamentary candidates.

The letter suggests that money from Labour funds be set aside to ensure that more candidates come from "manual working backgrounds". At the last election more than 80% of Labour candidates came from professional backgrounds and just 9% from manual working backgrounds.

Yesterday Labour's national executive committee (NEC) agreed that, for the first time ever, a new category of registered party supporters can have a say in electing the leader. Under the plan, registered supporters would get 10% of the vote, so long as at least 50,000 sign up. The NEC also agreed to conclude talks with the unions by the end of March next year on how to reform policymaking to ensure it becomes "more dynamic, open and democratic".