The number of people owning up to using hand-held mobiles at the wheel has fallen from 36% in 2006 to the current figure of 13%.
But the poll of 1000 drivers also showed the number using hands-free mobiles while driving has risen from 22% in 2006 to 38% now.
Using hand-held mobiles at the wheel has been illegal for a decade.
The survey, by road safety charity Brake and insurance firm Direct Line, found 68% of those questioned agreed it was dangerous to use any type of phone while driving, but only 36% supported a ban on hands-free mobiles, while 4% said all phone use should be permitted.
Brake wants a total ban on mobile phone use by drivers.
Julie Townsend, the charity's deputy chief executive, said: "It is shocking that, 10 years after the ban, one in eight drivers continues to flout the law and put lives in danger by using a hand-held mobile at the wheel.
"Just as worrying is the widespread belief that using a hands-free kit is a safe alternative. It's not. Using a hands-free phone while driving can end and ruin lives just as surely as using a phone hand-held, and no phone call or text is worth a life."
Rob Miles, of Direct Line, said: "It is hoped that as drivers become more aware of the dangers inherent in the use of mobiles whilst driving, it will become as much of a social taboo as drink-driving has become."