The plea came at the launch of a new campaign, called 'Shut Up Britain!', by road safety organisation Brake.
It coincided with a warning by Transport Minister David Jamieson that legislation may force a ban if drivers do not put safety before phone calls.
Brake's campaign demands the Government goes ahead with legislation to ban the use of mobile phones while driving after a survey of Britain's biggest 30 companies revealed 77% do not ask drivers to refrain from phone use while behind the wheel.
Brake congratulated companies that did have a policy on the issue, including AstraZeneca UK, BP Retail UK and Direct Line.
The campaign is backed by victims of accidents caused by drivers who were using their mobile phones on the road, including Susan Penney, from Grimsby.
She was a passenger seriously injured in a company car when the driver collided with an oncoming vehicle while talking on a mobile phone.
Businesses that have already banned use of mobile phones while driving have thrown their support behind the campaign.
Dominic Burch, road safety campaign manager at insurance company Direct Line, said: 'We would like the Government to go one step further and actually make it a specific offence to use a hand-held mobile phone while driving.
'Until that happens, we believe dangerous drivers will continue to use their phones behind the wheel, putting themselves and others at risk.'
In Parliament last week, Jamieson told MPs the message had already been heard.
He said: 'If drivers cannot be persuaded not to use mobile phones while driving, the Government accepts that new legislation may be necessary.'