A total of 360,000 holidays are said by the CAA to be eventually refunded.
It urged people to "try back again later today".
The problems were apparently still ongoing at lunchtime on Monday, with the CAA saying on Twitter at about 12.40pm: "We are receiving an unprecedented level of traffic to the website now so please try again later if you are not now able to get through the system". The agency expects at least 360,000 ATOL-protected bookings will need to be refunded, covering trips for more than 800,000 people.
Refunds for Thomas Cook customers will either be handled by the Civil Aviation Authority from Monday (7 October) or by banks and card providers, so we would urge anyone waiting to claim their money back to ignore alternative websites and unsolicited calls or texts promising a refund.
Around 60% of the costs for the repatriation will be picked up by CAA, with the remainder being funded by the Government.
People who booked holidays with Thomas Cook that never happened can now apply online to receive a refund.
About 140,000 Thomas Cook passengers have been brought home from around the world on 150 aircraft during the past two weeks.
The final Operation Matterhorn flight - the program's 746 - is scheduled to arrive at Manchester Airport (MAN) on Monday with 392 passengers onboard.
The vast majority of Thomas Cook's holidays were covered under the Air Travel Organiser's License scheme.
What was described as the largest-ever refunds programme of its kind was launched by the UK's Civil Aviation Authority on Monday - but many customers were left angry and frustrated after receiving error messages when attempting to submit their claims.
"I want to thank everyone who has played their part in delivering this enormous undertaking, including the passengers we flew home for bearing with us as we undertook this complex operation, " he said. The programme is not over yet and we still have work to do, but I would like to say a honest thank you to everyone who has played their part in this operation so far.