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People are being asked to think twice before providing personal information on the phone.
The warning comes following several reports of callers pretending to be from Medway Council and asking for sensitive information.
The calls are not from the local authority and are thought to be a scam.
Therefore, any residents receiving these calls should not provide any details, and contact the council as soon as possible to report the call.
Judith Lane, of Lodge Hill Lane, Chattenden, is just one of a handful of residents in Hoo and the surrounding area that has been targeted in recent weeks.
She said: “I first heard about these calls on Facebook and then it happened to me. A man called and said he was from Medway Council, but because I had heard of the scam previously I told him I didn’t believe him and then he hung up.
"It is a scam and we advise that no personal information is given out" - Cllr Peter Hicks
“People that aren’t aware of this happening may not realise that this is a scam, so the word needs to spread and everyone needs to know.
“They could be targeting elderly people, I’m retired myself, but luckily I already knew this was happening.”
From reports received so far, the caller has been asking for information such as individuals’ NHS numbers and information about accidents they or their family members may have been involved in.
Cllr Peter Hicks, who is in charge of community safety, said: “I urge anyone who receives one of these calls or similar, to contact the council on 01634 333333 or call the non-emergency police number, 101.
"We can assure residents that it is not Medway Council making these calls, instead it is a scam and we advise that no personal information is given out.”