The survey, conducted on behalf of Green Flag, also found that one in 10 motorists drive on less than five hours sleep at least once a month. From the 1,000 fleet drivers polled, 45% said they had driven while feeling tired.
The results come despite calls to tackle driving while tired which followed the prosecution of Gary Hart, whose vehicle crashed on to a railway line, causing the Selby rail crash. It was claimed he had fallen asleep because he had been driving while tired.
His Land Rover was hit by a 117mph express train, which then derailed into the path of a freight train, killing 10 passengers.
Following the latest Green Flag research, Mary Williams, chief executive of road safety charity Brake, said: 'These results are extremely disturbing. Tired drivers cause 20% of crashes on monotonous roads such as motorways.'
Brake is calling on the Government to introduce a range of initiatives including additional funding for media campaigns, continuous crash barriers on motorways and a review of the frequency of service areas on motorways.
It also wants it to make it a legal requirement for companies to have a risk management policy in place, implement an EU working directive for professional drivers, review the number of traffic examiners and make it a requirement for police to conduct thorough accident investigations.
Williams added: 'Drivers need to wake up to the fact that tiredness and driving are a potentially lethal combination. If you risk getting behind the wheel not having had enough sleep you risk killing yourself and other innocent road users.
'If you intend to drive, it is vital that you have a good night's sleep and take the necessary steps to combat tiredness on long journeys.'
The survey backs research carried out by Loughborough University's Sleep Research Centre, which has shown that after five hours' sleep, drivers have only a one in 10 chance of staying fully alert during a long journey.
A Green Flag spokesman added: 'Despite tiredness being a major cause of road deaths, the research demonstrates that a significant number of drivers still underestimate the dangers of fatigue.'