Some 39 per cent do not know that penalty points and fines will double to six and £200 respectively from Wednesday, according to a Co-op Insurance poll of 1,500 UK drivers conducted last week.
The firm described the findings as “very worrying”.
Drivers can be banned from Britain’s roads if they receive 12 points within three years, while new drivers can have their licence revoked if they get six points within two years of passing their test.
Stricter penalties for illegal phone use are being introduced by the Department for Transport following a series of high-profile cases and research suggesting the practice is widespread.
Twenty-two people were killed and 99 seriously injured in accidents on Britain’s roads in 2015 where a motorist using a mobile was a contributory factor, latest figures show.
In October, lorry driver Tomasz Kroker was jailed for ten years after killing a woman and three children by ploughing into their stationary car on the A34 near Newbury, Berkshire, while distracted by his phone.
Motoring groups believe a sharp decline in the number of drivers caught using a hand-held phone is partly due to police budget cuts affecting enforcement.
The Co-op Insurance survey found that almost a third (30 per cent) of drivers admit to using their phone behind the wheel and over half (54 per cent) do not believe the tougher punishments being introduced this week will deter offenders.
James Hillon, head of products at Co-op Insurance, said: “We welcome the penalty changes as anything which helps make our roads safer can only be a good thing.
“However, it is very worrying that a significant proportion of drivers are unaware of the changes given how significant they are.
“Whilst it seems as though the increase in penalties may encourage better behaviour, with a quarter now less likely to phone and drive, much of the driving population believe that the increase could have gone further.”
AA president Edmund King said: “We must stop this epidemic of texting/tweeting drivers by changing attitudes, and the campaign that kicks off this week is a big step in the right direction.”
Research last year from data obtained from the DVLA by car price comparison website Car Keys found Scots are the worst drivers in the UK for using their mobile phones while behind the wheel.