The report estimates that there is a dormant stock of several hundred million pounds, with a possible future flow of tens of millions of pounds a year.
It outlines a plan to transfer unclaimed assets in about 60 banks and building societies with total assets under £7bn to an "arm's length charitable organisation" for distribution.
It also proposes the banking industry sets up a central reclaim fund for assets, which would allocate payments of money that was claimed back by consumers.
In addition, the report renews the Government's 2005 pledge to reinvest dormant assets in the community.
"Building societies argue that their savings are locally generated, so should be given away locally," said Malcolm Hayday, chief executive of Charity Bank. "I sympathise, but where do you stop? And how do you know where the account holder would have wanted their money used?"