More than 200 drivers a day were caught using a mobile at the wheel immediately after tougher penalties for the offence came into effect, figures show.
UK police caught almost 6,000 drivers using their devices while driving in the four weeks after 1 March.
The numbers were obtained by the Press Association under the Freedom of Information (FOI) Act.
In March, the penalty for using a phone while driving doubled to £200 and six penalty points.
Under the rules, new drivers caught using a phone within two years of passing their driving test will have their licence revoked altogether.
The high number of people breaking the law means the "key message still isn't sinking in", said Steve Gooding, director of motoring research charity The RAC Foundation.
"Driving is a safety-critical activity that requires our full attention. Hands need to be on the wheel and eyes looking out of the windscreen, not down at the phone screen," he added.
Road safety charity Brake called for the £200 fine to be "significantly increased" to deter offenders.
"Driver distraction is a growing menace and it's worrying that drivers don't seem to be getting the message," said Brake spokesman Jack Kushner.
AA president Edmund King said changing drivers' attitudes would take time:
"We know we can't change the attitudes and actions of all drivers overnight.
"We now have stricter penalties so need to continue with education campaigns (including driving schools) plus more police enforcement."
Details of incidents reported by police:
- A man doing his online banking while driving along the M5 motorway near Birmingham
- Norfolk Police stopped a woman who was responding to a message about her lost puppy being found
- A man using his phone while driving a 7.5-tonne lorry around a roundabout in Bournemouth
- A school minibus driver with 10 children on board in Manchester using his phone while driving
- More than a third of the 5,977 incidents reported occurred on London's roads making it the place with the highest number of offences
Pressure to prevent drivers using phones intensified last year in the wake of several high-profile cases as well as research indicating it was widespread.
In October, lorry driver Tomasz Kroker, who killed a mother and three children while distracted by his phone, was jailed for 10 years.
In 2015 - the latest year for which figures are available - 22 people were killed and 99 seriously injured in accidents where a driver was using their phone.