Barclays today announced plans to compensate tens of thousands of customers who were mis-sold payment protection insurance on a no-quibbles basis.
The group, which has set aside £1 billion to cover its redress programme, said anyone who complained on or before April 20 would have their complaint settled in full as a "gesture of goodwill".
But other consumers may have to wait for longer before they find out if they will receive any money back, after the City watchdog announced an extension to the timeframe in which banks must deal with PPI complaints.
The Financial Services Authority said it had granted a temporary extension to the time limit in which Lloyds Banking Group, Royal Bank of Scotland and Barclays had to deal with complaints on the issue due to the huge backlog and high volume of new complaints that the groups face.
Instead of having to deal with the complaints within eight weeks, the banks will have until August 31 to resolve mis-selling claims that were put on hold during the judicial review.
They will also have 16 weeks in which to handle complaints that were received after the judicial review but before the end of August and 12 weeks to process ones received between the end of August and the end of the year.
The FSA said it had granted the extension to ensure that complaints were handled properly, but taxpayer-backed Lloyds Banking Group and RBS are likely to come under pressure to follow Barclays' lead and settle all claims in full.
Peter Vicary-Smith, chief executive of Which?, said: "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.
"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."
The banking industry last month dropped its legal challenge over whether new FSA rules on PPI mis-selling claims could be applied retrospectively.
The move means more than three million people are in line for compensation, expected to cost firms between £7 billion and £9 billion.
Lloyds Banking Group, whose brands include Halifax and Lloyds TSB, has made the biggest provisions for compensation at £3.2 billion, while RBS, which includes NatWest, has set aside £850 million and HSBC has made provisions for 440 million US dollars (£270 million).
A Barclays spokeswoman said: "We have said before that when we get things wrong, we apologise, and work hard and work fast to put them right as quickly as possible.
"In recognition of the delay customers have experienced whilst awaiting the outcome of the High Court judgment, we can confirm that we are contacting customers whose complaint was put on hold on or before April 20 with an offer to settle their complaint in full as a gesture of goodwill."
Andrew Hagger, of financial website Moneynet.co.uk, said: "The decision from Barclays to pay out on all PPI claims submitted before April 20 is a common sense move and hopefully one that other lenders will follow.
"Not only will the 'no quibble' policy enable compensation to be paid more quickly, it will also slam the door in the face of the growing band of claims management companies looking to make a fast buck at the consumer's expense."
PPI covers debt repayments if the holder is unable to work due to an accident or illness, or if they lose their job.
It looks set to become the biggest mis-selling scandal the UK has ever seen, with final PPI compensation likely to dwarf the £4.5 billion paid to people who were wrongly sold personal pensions and the £2.7 billion paid to victims of endowment mis-selling.