The Big Society Bank is likely to have assets of between £60m and £100m by its planned opening date next April, according to the government's advisers on the project.
The money is to come from dormant accounts in banks and building societies, which have been estimated by the British Banking Association to contain £400m. Some third sector finance specialists estimate the sum could be ten times that.
A spokesman for the Office for Civil Society said that the Co-operative Bank, which is administering the process of reclaiming money from dormant accounts, had estimated that the bank is likely to have obtained only £60m to £100m of unclaimed assets by April.
He said this was because of practical difficulties such as tracking down owners of potentially dormant accounts.
In his big society speech in Liverpool today, the Prime Minister said that the Big Society Bank would receive every penny from unclaimed assets, which in combination with additional funds from the private sector would unlock "hundreds of millions of pounds" for the sector.
The Labour government had said its proposed social investment bank, a similar proposal to the Big Society Bank, would have been third on the list of recipients of dormant bank account money, after youth and financial inclusion services.
The bank is intended to provide wholesale finance to intermediaries that lend to charities, social enterprises and community groups.
Existing social lenders said they were pleased with the planned structures.
Malcolm Hayday, chief executive of Charity Bank, said: "We have called for the Big Society Bank to be a wholesale provider of finance to existing independent intermediates, so we are pleased that this seems to be the case.
"The involvement of current social investment organisations will provide the most effective way to leverage the impact of the money available and therefore multiplying the effect of the funds available."
Bernie Morgan, chief executive of the Community Development Finance Association, said: "We very much welcome the Big Society Bank. With disadvantaged communities around the country crying out for investment, it is essential that the government launches the bank in time for its ambitious April 2011 deadline."