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Police were called in after travellers moved onto playing fields.
Members of the public reported several vehicles had been driven on to Gillingham Green, a public park off Grange Road, Gillingham, on Friday evening.
Police confirmed they had been notified, adding: "As is the normal process for traveller incursions, the matter will be a civil issue for the landowner to address."
James Brown, Head of Regulatory Services at Medway Council, said: “We are following a civil legal process to move the group on as quickly as possible.”