The British Bankers' Association (BBA) has drawn a line under its legal fight to avoid PPI mis-selling payouts.
Last month, the High Court ruled banks must look again at hundreds of thousands of PPI cases, rejecting a judicial review brought by the BBA against the FSA.
The BBA had indicated it may appeal but today's decision to admit defeat means consumers could be in line for billions in payouts for being mis-sold the policies.
In a statement, the BBA said: "In the interest of providing certainty for their customers, the banks and the BBA have decided that they do not intend to appeal.
"We continue to believe there are matters of important principle which we will be taking forward in other ways with the authorities."
The BBA's decision come after both Barclays and Lloyds indicated they will not participate in any legal challenge, setting aside billions of pounds for payouts.
The FOS has been receiving around 5,000 PPI complaints per week in recent months and has warned it could be overwhelmed if banks continue to be uncooperative.
Natalie Ceeney, chief ombudsman, said: "It's very good news the banks will not be appealing the High Court's clear-cut judgment, which endorsed the ombudsman's and the FSA's approach to PPI complaints.
"We are pleased banks will now be dealing with their customers' complaints. Consumers should come to us at the ombudsman if they're unsure about what to do next.
"Meanwhile we will be working with the banks, over the coming weeks, to ensure that consumers' complaints are dealt with fairly and promptly."
