A total of 7% have actually fallen asleep while driving, the poll by road safety charity Brake and insurance company Direct Line found. Also, 49% said they had driven after less than five hours of sleep.
The poll revealed 31% have "head nodded"while at the controls, with 45% of male drivers owning up to this. Just 2% of women drivers admitted falling asleep at the wheel but 14% of male motorists confessed to this.
Men (55%) were also more likely than women (45%) to drive after less than five hours' sleep.
Brake said research has shown tired driving kills at least 300 people on UK roads every year. Deputy chief executive Julie Townsend said: "The fact that so many drivers have head-nodded at the wheel is horrifying."