The government-backed savings institution National Savings and Investments is preparing to make large payouts after admitting mistakes that left customers without money to which they were entitled.
Ministers will discuss the issue in Parliament as officials try to work out the final bill.
Officials estimate the problems could affect roughly 37,000 customers.
NS&I, which looks after about 24 million people and more than 22 million Premium Bond accounts, has apologised to anyone who experienced poor service, particularly during bereavement.
Complaints range from delayed or withheld Premium Bond prize payments to accounts being mislaid.
Some families say they only discovered missing funds after legal intervention and were forced to pay for lawyers to recover what was owed.
One long-standing saver told the BBC his date of birth had been recorded incorrectly for decades, and he believes the error prevented account access for years.
He warned that, had he died, his will might not have been executed because of the incorrect records.
Treasury staff are working alongside NS&I to establish how much compensation is required.
Analysts point to the institution’s multi-billion-pound modernisation programme, which has fallen behind schedule, as a possible factor in the operational failures.
Industry figures have urged NS&I to act quickly to rebuild trust among investors and savers.
Lawmakers are also expected to press ministers on whether taxpayers could ultimately cover the cost of any settlement.
Specific cases publicised in the press include a daughter who was not informed about bonds held by her late mother and a saver who lost track of around £2,000 in Premium Bonds.
In another instance NS&I refunded a family for tax, interest and legal fees after accounts connected to an investment portfolio were misplaced.
Separately, the Treasury has noted that around £100 million in Premium Bond prizes remain unclaimed, adding to concerns about record-keeping and prize distribution.
NS&I and the Treasury are due to provide further detail when the pensions minister addresses the House of Commons.
The BBC has sought comment from NS&I as the organisation works to quantify payouts and resolve outstanding customer cases.
