Research into accident claims from more than 300,000 fleet car and commercial vehicle drivers revealed a third came from parking accidents, with 65.43% occurring at 9mph or less.
These figures represent a 3% increase in low-speed accidents compared to a year ago and highlight the need for fleet decision-makers to focus on simple skills and awareness training for drivers.
Motor claims management firm Town & Country Assistance, which carried out the research, wants fleet decision-makers to warn drivers of the potential for prangs when parking and investigate the benefits of driver training.
Theodore Agnew, chief executive of the firm, said: 'There is a certain stigma attached to parking incidents. Drivers do not like to admit they have had trouble parking their vehicles, so it is impossible to be certain about the exact percentage of motor claims that arise from parking incidents.
'However, what is certain is that almost two-thirds of all motor claims now arise from vehicles which are either stationary, whether parked or stuck in traffic, or travelling at very low speed, whether parking or turning to deliver goods.'
Congestion is partly to blame for the increase in slow speed accidents, as drivers in traffic jams brake too late and smash into the driver in front.
But he added: 'The large number of people carriers and 4x4s and other large vehicles with more blind spots than smaller vehicles are another factor, as is the fact that many car parks were not designed for vehicles of that size.'