The Royal Society for the Prevention of Accidents says six deaths on Britain’s roads have been linked to the use of telephones.
Its president, Lord Davies of Oldham, introduced measures to the House of Lords on Thursday to make it a specific offence to talk on a hand-held mobile while in charge of a moving vehicle.
Rospa says its own opinion polls suggest 84% of the public back such a ban.
However, the ban is unlikely to become law without government support.
Lord Davies said: “I have a long-standing interest in such matters and believe it is very dangerous to use a hand-held phone while at the wheel.
“A specific offence would make it clear to drivers that it is wrong, as there seems to be some confusion among motorists at present about where they stand legally.”
Rospa says its research shows even hands-free mobile phones make driving more dangerous and increase drivers’ risk of having an accident.
Its director of safety policy, John Howard, said: “It is much safer for drivers not to use any type of mobile phone when they are on the move, because a telephone conversation is a major distraction from the driving task.”
Mr Howard welcomed the initiative to change the law, saying it would make it clear to motorists they were putting themselves and others at risk if they used a phone whilst driving.
“Police have used a variety of offences to take action against mobile phone users, but a specific offence would mean there would be no excuse for a driver seen using a mobile phone at the wheel,” he said.