The banker trade body had until tomorrow to appeal the ruling which will see thousands of customers receive financial redress from the banks that sold them unsuitable PPI products they didn't need.
The BBA said today: "In the interest of providing certainty for their customers, the banks and the BBA have decided that they do not intend to appeal.”
The news comes after Lloyds Banking Group said last week it had set aside £3.2bn to compensate customers mis-sold PPI cover and would not join the BBA in any appeal.
Barclays announced yesterday it would set aside £1bn to cover claims and also pulled support for the BBA appeal.
Moneynet’s Andrew Hagger said: “Following the announcement from Lloyds TSB last week, it was inevitable that the other banks and the BBA would be left with little choice but to follow suit.
“Let’s hope the banks provide sufficient manpower to ensure the repayment of premiums is made promptly and without fuss. It’s time to draw a line under this sorry saga and for the banks to win back customer trust by concentrating on delivering consistently high levels of service and moving away from the pushy sales culture.”
The BBA had argued that the retrospective imposition of PPI mis-selling rules by the Financial Services Authority and the Financial Ombudsman Service set a dangerous precedent.