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Travellers have pitched up at the same site within a month.
A group descended on land in Rochester within weeks of an encampment leaving.
A Kent Police spokesman said: “Kent Police was called shortly after 6pm on Monday, September 2 and made aware of an encampment on land near Curtis Way, Rochester.
“Officers have since attended the site to assist the landowner and notices to leave the land have been served.”
A Medway Council spokesman added: "We are aware of the group and are following a civil legal process to move the group on."
Vandalism on the Warren Wood Estate in Rochester came on the same day the illegal encampment was reported at the nearby airfield, although there is nothing to suggest the two are connected.
Police confirmed that a fence and barrier were damaged on Monday evening at a building in Warren Wood Road.
A Kent Police spokesman said: “Inquiries to establish the full circumstances are under way.”
Early last month, about 20 caravans and as many vehicles camped out at a site nearby on land off Rochester Airport and the BAE Systems factory.
Under the Police, Crime, Sentencing and Courts Act 2022, police in England and Wales were given new powers to address harms caused by unauthorised encampments and new guidance was published.
It comes amid a chronic shortage of gypsy and traveller sites across the UK.