Around 75,000 people and companies who received one-off or regular payments from 2,000 businesses with accounts at the bank were inadvertently paid a second time on December 25.
Payments included wages or money from suppliers.
But because the cash has been sent to accounts at rival banks, it may be harder to retrieve and Santander will have to rely on the kindness of others to get back the cash.
The banks can retrieve the cash but some are said to be worried that it may already have been spent and they do not want to risk pushing customers into overdrafts.
According to the Times, one bank said it would be reluctant to take the money back if it meant the account holder was tipped into overdraft as a result.
Pay UK, which runs the main payment systems in the UK, is holding talks on how to reverse the payments and some cash has already been recovered.
Under the "bank error recovery" process, Santander is talking with rivals and approaching some customers directly.
A spokesman said: "We're sorry that, due to a technical issue, some payments from our corporate clients were incorrectly duplicated on the recipients' accounts.
"None of our clients were at any point left out of pocket as a result and we will be working hard with many banks across the UK to recover the duplicated transactions over the coming days."
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