The City watchdog has extended the amount of time the banks have to settle claims for mis-selling payment protection insurance while Barclays has pledged to fully compensate thousands of customers.
Barclays has committed to settle tens of thousands of outstanding claims over the scandal, putting pressure on rivals to follow suit.
The Financial Services Authority said it would extend the timeframe for banks to deal with claims that had been put on hold beyond the eight weeks they have in the past been allowed.
In May, Lloyds, Barclays, Royal Bank of Scotland and HSBC unveiled more than £5bn charges to cover compensation for PPI mis-selling.
Lloyds bore the brunt with a £3.2bn provision.
Barclays, which estimated it would take a £1bn compensation charge, said all customers who had made a complaint by April 20 - when banks lost a key court ruling - would get an offer to settle their complaint in full, and receive annual interest of eight per cent.
The bank said it will work to clear the backlog of more recent claims.
"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," said Peter Vicary-Smith, head of consumer group Which?
PPI insurance policies were typically taken out alongside a personal loan, mortgage or purchase to cover repayment if the borrower was unable to pay due to unemployment, sickness or accident.
But the policies were often mis-sold to self-employed or unemployed people who would not have been able to claim.
They were also mis-sold to consumers who did not realise they were taking out such a policy and a court ruled that the banks were at fault.
City A.M. Reporter