Thomas Cook customers who had booked holidays with the firm have submitted 40,000 refund forms in the first hours of operation since a special website for the process was launched.
The UK Civil Aviation Authority said the process was now running smoothly after initial delays caused by high demand.
Customers had complained they had tried to submit the claim form several times, but kept receiving error messages.
The CAA blamed "unprecedented demand" and urged users to try later.
In total, the aviation regulator has to refund some 360,000 customers.
It will take 60 days for people to get their money back.