More than 200,000 savers were caught up in the Icesave collapse
Organisers of the UK's deposit protection scheme say there is "no obvious reason" why some Icesave customers have yet to reclaim money.
Some 188,738 people have used the online claims system to retrieve money trapped when the bank collapsed.
But 9,481 customers eligible to use the electronic payment system run by the Financial Services Compensation Scheme (FSCS) have still failed to do so.
The repayment process began in November and each case can take up to six weeks.
Icesave - the internet arm of Landsbanki - collapsed in October, but the UK government said no savers in the UK would lose money.
Although the Icelandic government agreed to pay out the first £18,000 to savers, the repayments are being paid out through the FSCS.
Those customers who can claim through the electronic payment system have until 30 December to do so, with their money likely to be returned to them within five working days.
If they fail to do so, they will have to send in paper application forms to get their money, which could take a further six weeks to process.
Of the 16,846 people already lined up for this alternative paper application system, some 10,392 have received cheques through the post, leaving 6,454 still waiting or yet to claim through this method.
A spokeswoman for the FSCS said there was "no obvious reason" that some savers were yet to claim.
"More than 90% of people were able to use the electronic process," said Loretta Minghella, chief executive of the FSCS.
Some customers only had a few pounds in an account and so might not bother getting it back, although others were owed what was described as "an amount you would want to reclaim".
Some with fixed-rate accounts had been waiting until the maturity date before claiming, the spokeswoman said. Instead of moving their money elsewhere, they are leaving their cash to accumulate more interest.
Meanwhile, insurer Norwich Union said it had returned £10m of unclaimed cash to its customers.
It appointed a tracing company to return cash from life insurance policies that had matured but had not been claimed by policyholders.
Last year Norwich Union, which is part of Aviva, said it intended to return £40m of unclaimed assets to 40,000 customers.
"There is often a good reason the money has remained unclaimed, such as changes of address or lost policies," said chief operating officer Cathryn Riley.
"The issue of unclaimed assets affects the whole industry and it is not going to go away on its own. We are taking decisive steps to address the matter and we encourage the rest of the industry to follow our lead."