Both pilots on a Airbus passenger plane were asleep at the same time with the UK-operated aircraft flying on autopilot.
One of the pilots indicated in a report to the UK's Civil Aviation Authority (CAA) that the pair nodded off after both had only five hours sleep in the previous two nights.
Details of last month's incident, on August 13, come at a time when UK pilots' organisation Balpa is unhappy at proposed European changes to flight-time regulations.
A CAA spokesman said: "This was a serious incident but an isolated one. I think lessons will be learnt from this. We are circulating this report within the industry.
"We don't know why the pilots had had so little sleep before this flight. They were taking it in turn to have rest periods, with the one always checking the autopilot and it looks as if both fell asleep at the same time."
Details of the incident, logged by the CAA as a mandatory occurrence report, were obtained by a news agency which had asked for incidents of pilot fatigue.
The CAA did not say which airline was involved nor where the aircraft, an Airbus A330, was travelling.
The report was headed: "Flight crew suffering from symptoms of severe fatigue."
It went on: "Reporter (almost certainly the captain) suggests both members of flight crew had only five hours sleep in two nights due to longer duty periods with insufficient opportunity to sleep.
"Both crew rested for 20-minute rotations and fell asleep."
Balpa said: "In the UK we have a strict set of flight safety rules which govern how long and how often a pilot can fly before their performance is impaired.
"The EU is proposing more permissive flight safety rules which would allow pilots to be flying aircraft whilst dangerously fatigued. These rules were not developed using scientific data and could have a grave impact on the safety of UK aviation."
Balpa said the EU proposals were "flawed in many areas", with pilots being legally allowed to land an aircraft having been awake for 22 hours, pilots operating longer-haul flights (such as west coast US) with only two crew rather than the current three, and pilots possibly being forced to work up to seven early starts in a row.
The CAA said today: "We understand that Balpa are not happy with the proposals but we think overall it is a good package and not much different to what we have now."
Balpa said last month's incident "comes as no surprise", adding that it had "repeatedly warned the CAA of the risk of both pilots falling asleep, including in a letter to each member of the CAA board last year".
Balpa general secretary Jim McAuslan said: "British pilots want to make every flight a safe flight and tiredness is the biggest challenge they face.
"As the regulator responsible for UK flight safety, the CAA has been far too complacent about the levels of tiredness among British pilots and failing to acknowledge the scale of the under-reported problem.
"In fact, the CAA and Government are backing EU cuts to UK flight safety that will increase tiredness among pilots and the risk of dangerous incidents."
A CAA spokesman said: "The new European rules will increase our oversight role of airline operators and place firm obligations on airlines to introduce comprehensive fatigue management policies and monitoring systems.
"This will maintain the UK's current high safety levels and will increase safety levels in some other EU states."