The authority has so far settled 320,000 claims, 95% of those received to date, at a value of more than £310 million in Atol payments. This is up from 90% at Christmas.
A further 10,000 claims remain outstanding, which the CAA said were being processed "as a matter of urgency".
It is also yet to receive claims for "thousands" more forward Cook bookings and is urging anyone with a valid claim but has not yet lodged it to do so as soon as possible.
The CAA said delays repaying certain claims "in most cases" were a result of claimants providing details that do not exactly match Cook’s booking records.
It initially set a target of paying all valid claims within 60 days of receipt. "We have a dedicated team working through the remaining claims in order to support consumers and process Atol payments as quickly as possible," said the CAA in an update issued on Wednesday (8 January).
Chief executive Richard Moriarty said: “While more than 95% of people who have made a claim have now received their Atol payments, we are sorry some are yet to receive payment. We are continuing to work through this enormous operation as quickly as we can as we understand customers who have seen their future holidays cancelled will want to receive payment as soon as possible.
“We acknowledge it has taken longer than we had hoped to make payments to the remaining consumers. We have a dedicated team working to process the most complex cases that need additional support and all consumers with outstanding claims should hear from us by the end of this week to receive an update on their claim and any next steps required.
"If we request further information, we would encourage consumers them to respond as quickly as possible as we cannot process any payments until this information has been received.”
The refund process is set to be the largest in the history of the Atol scheme.
