According to the British Airline Pilots' Association (BALPA), 56% of 500 commercial pilots admitted to being asleep while on the flight deck and, of those, nearly one in three said they had woken up to find their co-pilot also asleep.
Pilot exhaustion grabbed the headlines this week when a newspaper reported two pilots on a British long-haul flight fell asleep in the cockpit, leaving the packed jet travelling unsupervised on autopilot.
The survey, released by BALPA, came ahead of a vote in the European Parliament on Monday on new rules that could replace British regulations.
BALPA, a trade union for pilots, voiced concerns that these proposed changes would water down British safety standards.
The rule changes would mean that pilots could work a maximum of 110 hours in a two-week period, more than the 95-hour limit under British regulations, and at night could be expected to fly for up to 11 hours, against a current 10-hour limit.
"Tiredness is already a major challenge for pilots, who are deeply concerned that unscientific new EU rules will cut UK standards and lead to increased levels of tiredness, which has been shown to be a major contributory factor in air accidents," BALPA General Secretary Jim McAuslan said in a statement.
The proposals, devised by the European Aviation Safety Agency to harmonise the rules regarding pilots' hours across the European Union, would also mean they could be called to work at any time on their days off. Currently, restrictions are in place to help them plan their rest on days off.
The survey of pilots, by pollster ComRes, found 84% of respondents believed their abilities had been compromised over the last six months by tiredness with almost half saying pilot exhaustion was the biggest threat to flight safety.
British lawmakers, in a report published earlier this month, expressed concern that the new European rules set the limit for the flight duty period at night too high.
But the Association of European Airlines, which represents 31 European airlines, urged support for the proposals, saying they would ensure all airlines followed the same rules.
"The new ... rules would ensure that Europe will continue to have one of the strictest rules in the world, even stricter than today," the body's acting Secretary-General Athar Husain Khan said in a statement.
The Civil Aviation Agency, Britain's aviation regulator, dismissed worries about the new rules.
"We think the new European flight time limitation regulations maintain the UK's current high safety levels, and will actually increase safety for UK passengers travelling on some other European airlines," it said in a statement.