"Socially responsible" savers could be encouraged to put their money into "big society" ISAs under plans being announced to show how the money will be found to fund David Cameron's vision of a volunteering renaissance.

The plans are to be unveiled as the prime minister makes a speech to try to relaunch his big society idea in the face of growing claims that volunteering will never thrive in an era of harsh public spending cuts.

The Cabinet Office is publishing plans to attract capital into the social investment market, including £400m from dormant bank accounts and – eventually – further sums from individuals and institutions like pension funds that might be prepared to invest routinely in social enterprise.

Social investments are already worth £200m a year but the Cabinet Office says this market is "embryonic and needs support". Ministers want to expand it to the point where "socially responsible everyday savers" start investing their money in "social ISAs and pension funds", although they also stress that this is a long-term aspiration.

The Cabinet Office paper, Growing the Social Investment Market: A vision and strategy, attempts to answer critics who say the cuts will kill volunteering by suggesting that social investment could eventually become as important a source of charity funding as traditional donations and the state. The government is also setting up a "big society bank" to fund social enterprises. It will start operating in April with up to £100m of the £400m from dormant accounts being made available this year. Banks are going to lend it another £200m on commercial terms.

The prime minister's other big society relaunch initiatives have included the appointment of Charlotte Leslie, a Tory backbencher, and Shaun Bailey, a youth worker and former Tory candidate, as big society ambassadors. Further announcements are due relating to the £100m transition fund for charities affected by the loss of government contracts and plans to train 5,000 big society organisers.

At an event in London, Cameron will insist that he will never abandon the concept because it is at the core of his political philosophy. "The big society is my mission in politics," he is expected to say. "And I am going to fight for it every day, because the big society is here to stay."

In his speech Cameron will resurrect his claim – once described by the London mayor, Boris Johnson, as "piffle" – that society is "broken". Lack of responsibility is to blame, he will say.

"I don't think this has happened because we've somehow become bad people. I think at its core, it's the consequence of years and years of big government. As the state got bigger and more powerful, it took away from people more and more things that they should and could be doing for themselves."

In an article in the Independent on Sunday, Ed Miliband argued that the big society was bound to fail because there was an inherent contradiction between wanting to build up the voluntary sector and cut the size of the state. "No one can volunteer at a library or a Sure Start centre if it's being closed down," the Labour leader wrote.

He said the big society was invented as part of an attempt to decontaminate the Tory brand and that the party was now "recontaminated" because "in the past week voters have seen more clearly than ever this Conservative-led government in its true colours: a single-issue government making huge sacrifices of the things we value on the altar of deficit reduction".

The former Tory cabinet minister David Mellor said the big society had gone down "like a lead balloon" at the election and that he could not understand why Cameron did not abandon the idea. But Francis Maude, the Cabinet Office minister, claimed the concept had been a public relations success.