David Cameron is launching a frantic bid to rescue his much-criticised plan for a "big society" as he promises to back the project with public money and new initiatives to help it survive savage government cuts and public scorn.

Writing exclusively for the Observer, the prime minister confronts his critics head on and insists that he will never abandon what he believes is the defining mission of his premiership.

Cameron says the big society is not a government initiative, but the opposite – one that will see power handed from Whitehall to the people. "It has the power to transform our country," he declares. "That is why the big society is here to stay."

In a clear change of emphasis, however, he concedes that massive cuts to the budgets of local authorities, which in turn have had to pass them on to charities, could imperil the whole programme unless help is provided. "We understand that while the opportunity lies in the future the local authority cuts are happening now," he says.

As a result Cameron and his ministers will make a blizzard of big society announcements, including details of a £100m transition fund to help hard-pressed charities and social enterprises compete, for the first time, for government contracts.

To give the same organisations the working capital to set up and run community schemes, ministers will also lay out plans for a big society bank, whose reserves will be boosted by £200m from Britain's biggest high street banks.

The Observer can also reveal plans, to be announced within the next few weeks, to set up a big society university, backed by a multimillion-pound endowment, that will train future generations of community workers.

The first stage will be to announce which company or organisation has won a £20m tender to train an army of 5,000 big society workers over the next five years. The successful bidder will then, from 2015, have the contract to establish a permanent institute for community organising, which will hand out formal qualifications in community work.

Cameron's decision to, in effect, relaunch the big society follows stinging criticism from leading figures in the charitable sector and local government, who have said that attempts to foster a new spirit of philanthropy and volunteering are being fatally undermined by massive cuts to local government and charity incomes.

Dame Elisabeth Hoodless, who is stepping down as executive director of Britain's largest volunteering charity, Community Service Volunteers, sent a wave of near panic through Whitehall departments – which have all been asked to develop big society initiatives of their own – when she said spending cuts risked obliterating the country's existing army of volunteers.

In his article Cameron addresses Hoodless's claim head on. "I would ask people to look beyond the headlines and see a much bigger structural change in how the voluntary sector can work in future," he writes. "We are in the process of opening up billions of pounds' worth of government contracts so charities and social enterprises can compete for the first time. The scale of this opportunity dwarfs anything they ever had before."

Claims from Labour and others that talk of a big society is a way of concealing the cuts agenda are also rejected. "That is simply not true," the prime minister argues. "I was talking about social responsibility long before the cuts. Building a stronger, bigger society is something we should try to do whether spending is going up or down.

Controversially, banks that lend money to the big society bank will do so on a normal commercial lending basis, meaning they will make a profit.

Toby Blume, chief executive of community charity Urban Forum, told Civil Society magazine: "Why is this news? How does it differ from their normal lending to the voluntary sector? It is merely a bolt-on to their commitment to make finance available to small and medium-sized enterprises."

Separately, in an interview in the Observer marking publication of the freedom bill, deputy prime minister Nick Clegg says the coalition has made good progress in rolling back many of the intrusive laws passed by Labour.

However, he told Henry Porter people were right to continue to be suspicious of central diktat. "You shouldn't trust any government, actually, including this one. You should not trust government – full stop. The natural inclination is to hoard power and information."