Hampshire Police said the incident happened at around 4.15pm when officers in an unmarked Armed Response Unit noticed a vehicle narrowly miss their police car.
The officers’ attention was drawn to the driver, who was seen using a mobile phone at the wheel.
When the car was stopped, checks revealed the driver did not hold a valid driving licence or insurance.
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Officers were also alarmed to find a baby being carried in the arms of the child’s mother, unrestrained and without a suitable car seat.
The driver has been reported for summons and will appear before magistrates at a later date. The vehicle was seized at the roadside.
Police praised two young men who stopped to help officers fit a child car seat into a police vehicle, allowing the mother and baby to be driven home safely.