Since the Government introduced the ban late last year, growing numbers of fleets have reported drivers having near-misses with stationary cars parked in dangerous places by drivers answering calls.
Already it is claimed that one driver has died in a crash after another motorist stopped to answer their mobile phone, according to industry experts.
Fleets are now being encouraged to issue their drivers with advice and guidance policies and instruct them to use safe procedures to avoid more deaths.
Risk management company Peak Performance warns that the new law is causing problems on the roads with drivers making sudden and late decisions to pull off the road to answer phone calls, causing other motorists to swerve or brake hard to avoid them.
The firm has first-hand reports of drivers choosing stopping places that are potentially dangerous and make it difficult to get back on the road safely, such as field access points or on left-hand bends.
And despite drivers' efforts, most are still breaking the law, because you can only use a hand-held mobile phone when the vehicle's engine is switched off.
Peak Performance managing director James Sutherland said: 'It has been clear to us for some time that the new laws have had some unforeseen consequences that will cause problems for busy company car drivers and other road users on the move. Drivers' lives are at risk.
'Our advice is to severely limit the use of any phones while on the move and to wait until the end of the journey before retrieving messages and answering calls in a safe and appropriate stopping area.'
The warning comes as a new survey suggests that one in five fleets face prosecution because some motorists will continue to use a hand-held mobile phone for work purposes while driving.
Carried out by Halfords, it found a fifth of motorists illegally make business calls on their mobile phones while on the move despite last year's ban.
Halfords warns that this situation poses real problems for businesses which risk being found liable for their employees' recklessness, leaving them open to large fines. While many choose to ignore the law, others simply do not understand it.
Keith Scott, general manager, automotive, at Halfords said: 'The results of our survey clearly demonstrate the issue remains how to deter someone who doesn't expect to get caught breaking a law they don't completely understand.'
In November last year, Fleet News launched its PhoneSafe campaign, designed to raise awareness of the new law among fleet operators.
Click on the Phonesafe logo on the homepage for more details.
A month later, a company vehicle driver who caused a fatal accident after making a series of calls on his hand-held mobile phone while driving, was jailed for five years (Fleet NewsNet December 18, 2003).