The CAA says 99% of claims made so far by those who lost holiday bookings when Thomas Cook collapsed last September have been settled.
In total, the CAA revealed on Monday (20 April) it had received about 340,000 claims, worth nearly £350 million in payments under the Atol scheme.
It is the largest amount paid out under the scheme since it was introduced in the 1970s.
Claims are still coming in on a daily basis though, the CAA further revealed. The system will remain open until September, and anyone yet to lodge a claim are urged to do so as soon as possible.
CAA chief executive Richard Moriarty said: "This was a major operation that had to contend with huge complexity, incomplete data and fraudulent claims, and we acknowledge that some cases took longer to process than we would have liked.
"Nearly all claims have now been paid, and we appreciate the patience of former Thomas Cook customers as we tackled this immense task - the biggest ever managed by the Atol scheme."
Moriarty added: "I would also like to sincerely thank the dedicated teams we set up at the CAA to assist consumers with this claims process.
"Their work to get the right money back to the right people during the UK’s largest ever travel claims operation has been remarkable and hugely appreciated."