Police said the gang erected fake signs to make the work in the village of Eynsford seem genuine.
Investigating officer PC Robert Sayer, from the Sevenoaks District Neighbourhood Policing Team, said: “The local council has confirmed there were no works scheduled in the area at the time.
“We have spoken to witnesses who recall seeing men in the area but there could be others who noticed people or vehicles in the area who did not realise they were witnessing an incident which would later be reported as a crime.”
Kent Police have not ruled out a link between this incident and another which reportedly took place in Rochester on 22 November.
One man has been arrested and bailed to 14 January in relation to that incident.