A third of motorists are either unaware that a new law will make it illegal to hold a mobile phone while driving or will deliberately defy it, research by the RAC has suggested.

The findings were published yesterday amid concerns that the law, which comes into force on December 1, has not been publicised widely enough.

Safety campaign groups have also complained that the law should ban hands-free devices as well as hand-held mobiles.

The RAC found that a fifth of those who were aware of the new legislation did not know what it entailed.

Some 3% thought that "cradling the phone between your shoulder and your ear" would be legal, while 14% thought all use of mobile phones while driving was being banned.

Rebecca Bell, an RAC spokeswoman, said: "It is estimated that 500,000 motorists are on the phone in their cars at any one time.

"By our estimation, a good proportion of them - as many as 33% - will deliberately or inadvertently continue to break the law when the use of hand-held phones is prohibited."

The RAC said 5% of those surveyed intended to continue to use their mobiles illegally; 20% said they would stop using them completely in their cars.

Those who are caught breaking the law face fines of £30, or a fine on conviction of up to £1,000 for persistent offenders.

Manufacturers of hands-free kits are likely to see big dividends from the government's action. The RAC found more than 60% of those who knew about the change planned to buy hands-free equipment.

Critics of these systems argue that drivers are still distracted by the phone conversation, even with both hands free. A recent official study in Sweden found very little difference between hand-held and hands-free phones in tests of concentration.

The RAC advises drivers to use a fully-fitted car kit and keep calls to a minimum - it says arguments and delicate negotiations should not be attempted.