Of those who have been in an accident, more than half (53 per cent) said it was caused by the driver of the car being distracted - mainly by their phone or a passenger on their phone (32 per cent). And 12 per cent had been distracted because they were using an app while driving.
Direct Line surveyed 2,000 people and found that 27 per cent still feel it is acceptable to check their phone while stationary, such as in a queue of traffic or when waiting at a red light.
Gus Park, commercial director of motor at Direct Line, said: "Any form of distraction that takes the driver's eyes away from the road is risking their safety and that of their passengers and other road users."
He added that "cultural change" as well as proposed stricter penalties need to happen. "The government's Think! campaigns have done a great job of effecting this change in relation to drink driving and we are calling for them to refocus these campaigns on mobile distraction as a starting point to kick off the societal pressure for people to do the right thing."
It comes as police conduct a week-long crackdown on motorists who use their mobiles while driving. The operations will include dedicated patrols and messages on road signs.
The National Police Chiefs' Council said the campaign aims "to make 'driving distracted' as socially unacceptable as drink driving".
A similar week in May flagged up 2,323 offences.
It was announced in September that the government was planning to get tougher on drivers who use their phones on the go: it wants to double fines and points for using a mobile while driving.