The incident reportedly occurred on board an Airbus A330, operated by a UK-based airline, on August 13, shortly after the plane had taken off.
The co-pilots had allegedly agreed to alternate sleeping whilst leaving the plane on auto-pilot during the long-haul flight.
Instead, one of the pilots awoke to find they had both been asleep, and did not know how long the plane had been flying unsupervised for, The Independent reported.
The CAA was quoted as saying by the daily said: "A pilot reported he had worked consecutive duty periods with a seven-hour break.
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"But he had not been able to sleep for as long as he would have liked. He dozed and woke up to find that his co-pilot was also asleep," it said.
The report compiled by the CAA, which has chosen not to identify the airline involved, following the incident said flight crew were suffering from symptoms of "severe fatigue", according to the Sun.
"Perhaps the airline in question may have looked at their rosta or shift system as a result", the spokesperson said.
"In potentially critical safety situations like this, we aim to learn from what happened and ensure it will not happen again," he said.