The Dormant Bank and Building Society Accounts Act, which received royal assent last week, allows money from accounts that have seen no activity for 15 years to be transferred to causes such as youth centres, financial inclusion services and a social investment bank.
But financial experts who have studied the proposed system say the current estimate could be too low because it does not include accounts that are deemed to be 'live' because of technical changes to IT and banking regulations, but have actually not been used for more than 15 years.
The experts, speaking on condition of anonymity, said that calculations based on a similar scheme run in the Republic of Ireland since 2001, modified by factors such as population, inflation and GDP, suggest the UK figure could be closer to £4bn.
In Ireland, however, half the revenue was from post office accounts, which are not included in the UK model. Brian Mairs, a spokesman for the BBA, said "artificially inflated expectations" could be damaging to the third sector. "We'd advise the voluntary sector to make its calculations based on our current estimate," he said.
The Government has made it clear that its priority is to distribute dormant assets through the Big Lottery Fund for youth and financial inclusion services, with any surplus going to a social investment bank, which the voluntary sector sees as a priority.
Banks have agreed to participate in the dormant assets scheme on a voluntary basis, and the Government has pledged to review it after three years.
Louisa Darian, policy officer at umbrella body the NCVO, said she doubted whether banks would comply fully with a voluntary scheme.
"We're pleased the Government has agreed to carry out a review," she said, "but we're also disappointed it hasn't given itself reserve powers to enforce a compulsory scheme if necessary."