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Travellers who have appeared on Hythe Green say they plan to leave this weekend.
Ten caravans appeared at about 4.30pm on Thursday.
Some of the travellers spent a week in Greatstone before arriving in Hythe.
One of the travellers, who did not want to be named and is thought to be in his 60s, said they have permanent places to live in Redhill, Surrey and were touring Kent during the Easter holidays.
Residents living near the green have not reported any major disturbances but people we spoke to are not happy about the travellers’ presence.
One woman, who did not want to be named, said: “It worries me that they are driving their vehicles at high speeds across the grass, churning up the ground.
“By Monday morning there will be school children walking across it."
The travellers said they plan to leave on Sunday.
Hythe Town Council was expected to serve a notice to the travellers on Friday afternoon and is hoping a hearing will take place on Monday.
Judith McCormick, Hythe Town Clerk, said: “The council has had a similar situation last year. The Green is a public open space and is important it remains a public open space. It is not a place for people to live on.”
Police spokesman Rosy Alexander said: “We are aware of them, monitoring the situation and working with Hythe Town Council.”