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Magistrates have granted an application by Kent County Council for travellers to leave an illegal camp near the Cyclopark in Gravesend.
The authority served an eviction notice at Medway Magistrates Court yesterday afternoon after the group refused to obey a "direction to leave" order.
A spokesman said he expected the travellers to move away over the weekend.
Around 25 caravans moved on to the site near the eastern end of Cyclopark last week, sparking fears among residents and dog walkers.
Witnesses have reported fly-tipping, anti-social behaviour and vehicles driving dangerously fast across the park since the camp was set up.
Dog walker Alison Edwards said: "It does feel intimidating. People have seen cars hurtling through the fields.
"There has been little respect for the area with several trees chopped down. People have stopped from going up there."
Yesterday, another group of travellers were reported moving caravans on to Darenth Country Park, behind Darent Valley Hospital.
The camp has been reported to police who are monitoring the situation.