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The incident was captured on film, and shows the vehicle mount the pavement to overtake cars at one of the new traffic calming chicanes.
Councillor Julie Ward told Bucks Radio the police are aware of the footage, but are unable to do anything more at this time as the number plate isn't visible in the video.
(thanks to Matthew Grolimund for the video)
It happened on Wednesday afternoon, with locals insisting it's another example of how dangerous the new system is. Motorists have found signage on the A418 unclear, and there have been reports of accidents and near misses.
The traffic calming islands have been in place for several months, although the system is not yet complete. The road will be closed from April 7th - 18th for further work to take place.