Barclays has promised to compensate all customers to whom it sold payment protection insurance (PPI) and who made a complaint before 20 April.
The bank has decided to repay customers all their premiums plus interest of 8%.
The move will affect tens of thousands of customers, with the bank having previously put around £1 billion aside to cover the eventual cost it expects to have to pay out.
Any complaints the bank received after the automatic reimbursement date of 20 April will be reviewed 'on merit'.
Following the announcement, Peter Vicary-Smith, chief executive at Which?, said he hoped the 'no questions asked' approach would be adopted by other banks.
"Banks have a lot to do to re-build their reputation after over a decade of mis-selling PPI and then mishandling complaints about it," he added.
"It's fantastic to see Barclays stepping up in this way, acknowledging their mistakes and refunding customers what they're owed, no questions asked.
"Hopefully this will have a domino effect and other banks will follow suit - the sooner the banking industry can consign the PPI mis-selling scandal to the history books, the better."
Anyone who thinks they have been mis-sold PPI have been advised to complain direct to their bank and avoid costly claims management companies.
In a separate announcement, the Financial Services Authority has decided to extend the amount of time that three banks are allowed to deal with PPI complaints.
The regulator said Barclays, Lloyds Banking Group and RBS needed more time than the eight weeks that is usually allowed to deal with complaints because of the backlog that had built up and the high volume of new complaints.
Under the agreement, PPI complaints which banks put on hold during the judicial review must be settled by the end of August.
Complaints received after the review and before 31 August will have to be responded to within 16 weeks.
Any complaints received on or after 1 September and before 31 December 2011 will need a response within 12 weeks, before the normal eight week deadline resumes.
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