European MPs are due to vote today on changes to rules governing pilots' working hours.
The European Union wants to tighten and standardise time limits for flying which currently differ between member states.
But UK pilots' union Balpa says the new rules could see more pilots suffering fatigue, putting safety at risk.
Pilots claim the new limits are longer than currently exist in the UK, which the European Commission denies.
A survey by Balpa last week suggested more than half of pilots had fallen asleep while in charge of an aircraft.
The poll of 500 commercial pilots found that 56% admitted sleeping and 29% said they had woken up to find the other pilot asleep as well.
The survey came after it emerged two pilots on an Airbus were asleep while the aircraft was flying on autopilot.
Virgin Atlantic admitted on Thursday that it was the carrier involved.
But it denied that both the pilot and co-pilot had been asleep ‘simultaneously’ on the long-haul flight.
The Civil Aviation Authority issued a ‘clarification’ saying that while “both pilots were concerned they were suffering symptoms of severe fatigue and took controlled rest separately, they did not fall asleep at the same time”.
They were ‘tired but able to fly’ and well within legal limits, according to a Virgin spokesman, who told the Daily Mail: “We’re pleased the CAA has apologised and rectified its error.”
The CAA added that Virgin Atlantic is "now taking steps to adjust its rostering arrangements for flight crew".
The pilot and co-pilot were reported to have put the aircraft from Orlando to Manchester on autopilot during the flight in August. They then took it in turns to have 20 minutes of rest after only having five hours of sleep in the previous 36 hours.
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